Number Theory

Arithmetic Algebraic Geometry

11Gxx

  1. Amod Agashe, Kenneth Ribet, and William A. Stein, The Manin constant, Pure Appl. Math. Q. 2 (2006), no. 2, 617–636.[MR]
  2. Amod Agashe and William Stein, Visibility of Shafarevich-Tate groups of abelian varieties, J. Number Theory 97 (2002), no. 1, 171–185.[MR]
  3. Amod Agashe and William Stein, Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero, Math. Comp. 74 (2005), no. 249, 455–484 (electronic).[MR]
  4. Scott Ahlgren and Matthew Papanikolas, Higher Weierstrass points on X0(p), Trans. Amer. Math. Soc. 355 (2003), no. 4, 1521–1535 (electronic).[MR]
  5. Avner Ash, Darrin Doud, and David Pollack, Galois representations with conjectural connections to arithmetic cohomology, Duke Math. J. 112 (2002), no. 3, 521–579.[MR]
  6. Matthew H. Baker, Enrique González-Jiménez, Josep González, and Bjorn Poonen, Finiteness results for modular curves of genus at least 2, Amer. J. Math. 127 (2005), no. 6, 1325–1387.[MR]
  7. Arthur Baragar and Ronald van Luijk, K3 surfaces with Picard number three and canonical vector heights, Math. Comp. 76 (2007), no. 259, 1493–1498 (electronic).[MR]
  8. Mark Bauer, Edlyn Teske, and Annegret Weng, Point counting on Picard curves in large characteristic, Math. Comp. 74 (2005), no. 252, 1983–2005 (electronic).[MR]
  9. Tobias Berger and Krzysztof Klosin, A deformation problem for Galois representations over imaginary quadratic fields, J. Inst. Math. Jussieu 8 (2009), no. 4, 669–692.[MR/doi]
  10. Amnon Besser and Rob De Jeu, Li(p)-service? an algorithm for computing p-adic polyalgorithms, Math. Comp. 77 (2008), no. 262, 1105–1134.[MR]
  11. Peter Birkner, Efficient arithmetic on low-genus curves, PhD Thesis, Technische Universiteit Eindhoven, 2009.
  12. Nigel Boston and Rafe Jones, Arboreal Galois representations, Geom. Dedicata 124 (2007), 27–35.[MR]
  13. Hans-Christian Graf v. Bothmer, Finite field experiments (with an appendix by Stefan Wiedmann), Higher-Dimensional Geometry over Finite Fields, NATO Science for Peace and Security Series, D: Information and Communication Security, vol. 16, IOS Press, 2008, pp. 1–62.
  14. Irene I. Bouw and Brian Osserman, Some 4-point Hurwitz numbers in positive characteristic, preprint (2009), 23 pages.[arXiv]
  15. M. J. Bright, N. Bruin, E. V. Flynn, and A. Logan, The Brauer-Manin obstruction and Sh[2], LMS J. Comput. Math. 10 (2007), 354–377 (electronic).[MR]
  16. David Brown, The Chabauty-Coleman bound at a prime of bad reduction, preprint (2008), 10 pages.[arXiv]
  17. David Brown, Primitive integral solutions to x2 + y3 = z10, preprint (2009), 11 pages.[arXiv]
  18. Ezra Brown and Bruce T. Myers, Elliptic curves from Mordell to Diophantus and back, Amer. Math. Monthly 109 (2002), no. 7, 639–649.[MR]
  19. N. Bruin and E. V. Flynn, n-covers of hyperelliptic curves, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 3, 397–405.[MR]
  20. Nils Bruin, Visualising Sha[2] in abelian surfaces, Math. Comp. 73 (2004), no. 247, 1459–1476 (electronic).[MR]
  21. Nils Bruin, The arithmetic of Prym varieties in genus 3, Compos. Math. 144 (2008), no. 2, 317–338.[MR/link]
  22. Nils Bruin and Kevin Doerksen, The arithmetic of genus two curves with (4,4)-split Jacobians, preprint (2010), 22 pages.[arXiv]
  23. Nils Bruin and Noam D. Elkies, Trinomials ax7 + bx + c and ax8 + bx + c with Galois groups of order 168 and 8·168, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 172–188.[MR]
  24. Nils Bruin and E. Victor Flynn, Towers of 2-covers of hyperelliptic curves, Trans. Amer. Math. Soc. 357 (2005), no. 11, 4329–4347 (electronic).[MR]
  25. Nils Bruin and Michael Stoll, Deciding existence of rational points on curves: an experiment, Experiment. Math. 17 (2008), no. 2, 181–189.[MR/arXiv]
  26. Nils Bruin and Michael Stoll, Two-cover descent on hyperelliptic curves, preprint (2008), 19 pages.[arXiv]
  27. Nils Bruin and Michael Stoll, The Mordell-Weil sieve: Proving non-existence of rational points on curves, LMS J. Comput. Math 13 (2010), 272–306.[arXiv]
  28. Armand Brumer and Kenneth Kramer, Paramodular abelian varieties of odd conductor, preprint (2010).[arXiv]
  29. Yann Bugeaud, Maurice Mignotte, Samir Siksek, Michael Stoll, and Szabolcs Tengely, Integral points on hyperelliptic curves, Algebra Number Theory 2 (2008), no. 8, 859–885.[MR/arXiv]
  30. Kevin Buzzard and L. J. P. Kilford, The 2-adic eigencurve at the boundary of weight space, Compos. Math. 141 (2005), no. 3, 605–619.[MR]
  31. Robert Carls, Theta null points of 2-adic canonical lifts, preprint (2005), 18 pages.[arXiv]
  32. Robert Carls, Explicit Frobenius lifts on elliptic curves, preprint (2009), 26 pages.[arXiv]
  33. Robert Carls, Fast point counting on genus two curves in characteristic three, preprint (2010).[arXiv]
  34. Robert Carls and David Lubicz, A p-adic quasi-quadratic time point counting algorithm, Int. Math. Res. Not. IMRN (2009), no. 4, 698–735.[MR/arXiv]
  35. Antoine Chambert-Loir, Compter (rapidement) le nombre de solutions d'equations dans les corps finis, preprint (2006), 46 pages.[arXiv]
  36. Denis Xavier Charles, Complex multiplication tests for elliptic curves, preprint (2004), 13 pages.[arXiv]
  37. Denis Charles and Kristin Lauter, Computing modular polynomials, LMS J. Comput. Math. 8 (2005), 195–204 (electronic).[MR]
  38. Imin Chen, On the equation s2 + y2p = α3, Math. Comp. 77 (2008), no. 262, 1223–1227.[MR]
  39. Imin Chen and Chris Cummins, Elliptic curves with nonsplit mod 11 representations, Math. Comp. 73 (2004), no. 246, 869–880 (electronic).[MR]
  40. Robert F. Coleman and William A. Stein, Approximation of eigenforms of infinite slope by eigenforms of finite slope, Geometric Aspects of Dwork Theory. Vol. I, II, Walter de Gruyter GmbH &Co. KG, Berlin, 2004, pp. 437–449.[MR]
  41. B. Conrad, K. Conrad, and H. Helfgott, Root numbers and ranks in positive characteristic, Adv. Math. 198 (2005), no. 2, 684–731.[MR]
  42. Brian Conrad, Bas Edixhoven, and William Stein, J1(p) has connected fibers, Doc. Math. 8 (2003), 331–408 (electronic).[MR]
  43. Caterina Consani and Jasper Scholten, Arithmetic on a quintic threefold, Internat. J. Math. 12 (2001), no. 8, 943–972.[MR/link]
  44. Patrick Kenneth Corn, Del Pezzo Surfaces and the Brauer-Manin obstruction, PhD Thesis, University of California, Berkley, 1998.
  45. Gunther Cornelissen, Aristides Kontogeorgis, and Lotte van der Zalm, Arithmetic equivalence for function fields, the Goss zeta function and a generalisation, J. Number Theory 130 (2010), no. 4, 1000–1012.[MR/doi]
  46. J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, Cambridge, 1997, pp. vi+376.[MR]
  47. J. E. Cremona, T. A. Fisher, C. O'Neil, D. Simon, and M. Stoll, Explicit n-descent on elliptic curves. I. Algebra, J. reine angew. Math. 615 (2008), 121–155.[MR]
  48. J. E. Cremona, T. A. Fisher, C. O'Neil, D. Simon, and M. Stoll, Explicit n-descent on elliptic curves, II: Geometry, J. reine angew. Math 2009 (2009), no. 632, 63–84.[arXiv]
  49. J. E. Cremona, T. A. Fisher, and M. Stoll, Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves, Algebra and Number Theory 4 (2010), no. 6, 763–820.[arXiv]
  50. J. E. Cremona and M. P. Lingham, Finding all elliptic curves with good reduction outside a given set of primes, Experiment. Math. 16 (2007), no. 3, 303–312.[MR]
  51. J. E. Cremona, M. Prickett, and Samir Siksek, Height difference bounds for elliptic curves over number fields, J. Number Theory 116 (2006), no. 1, 42–68.[MR]
  52. John E. Cremona, A solution for note 84.35, The Mathematical Gazette 86 (2002), no. 505, 66–68.[link]
  53. John Cremona, The elliptic curve database for conductors to 130000, Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 11–29.[MR]
  54. John Cullinan, A computational approach to the 2-torsion structure of abelian threefolds, Math. Comp. 78 (2009), no. 267, 1825–1836.[MR]
  55. C. J. Cummins and S. Pauli, Congruence subgroups of PSL(2,Z) of genus less than or equal to 24, Experiment. Math. 12 (2003), no. 2, 243–255.[MR]
  56. Samit Dasgupta, Computations of elliptic units for real quadratic fields, Canad. J. Math. 59 (2007), no. 3, 553–574.[MR]
  57. Chantal David and Tom Weston, Local torsion on elliptic curves and the deformation theory of Galois representations, Math. Res. Lett. 15 (2008), no. 3, 599–611.[MR/arXiv]
  58. Christophe Delaunay and Christian Wuthrich, Self-points on elliptic curves of prime conductor, Int. J. Number Theory 5 (2009), no. 5, 911–932.[MR/doi]
  59. Daniel Delbourgo and Thomas Ward, The growth of CM periods over false Tate extensions, Experiment. Math. 19 (2010), no. 2, 195–210.[MR/link]
  60. Daniel Delbourgo and Tom Ward, Non-abelian congruences between L-values of elliptic curves, Ann. Inst. Fourier (Grenoble) 58 (2008), no. 3, 1023–1055.[MR/link]
  61. Lassina Dembélé, A non-solvable Galois extension of Q ramified at 2 only, C. R. Math. Acad. Sci. Paris 347 (2009), no. 3-4, 111–116.[MR/doi]
  62. Lassina Dembele, Matthew Greenberg, and John Voight, Nonsolvable number fields ramified only at 3 and 5, preprint (2009), 18 pages.[arXiv]
  63. Jan Denef and Frederik Vercauteren, An extension of Kedlaya's algorithm to Artin-Schreier curves in characteristic 2, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 308–323.[MR]
  64. Xavier Charles Denis, Complex multiplication tests for elliptic curves, Preprint (2004), 13 pages.
  65. Claus Diem and Emmanuel Thomé, Index calculus in class groups of non-hyperelliptic curves of genus three, J. Cryptology 21 (2008), no. 4, 593–611.[MR]
  66. Luis Dieulefait, E. Gonzalez-Jimenez, and J. Jimenez Urroz, On fields of definition of torsion points of elliptic curves with complex multiplication, preprint (2009).[arXiv]
  67. T. Dokchitser and V. Dokchitser, Computations in non-commutative Iwasawa theory, Proc. Lond. Math. Soc. (3) 94 (2007), no. 1, 211–272.[MR/doi]
  68. Tim Dokchitser and Vladimir Dokchitser, Root numbers of elliptic curves in residue characteristic 2, Bull. Lond. Math. Soc. 40 (2008), no. 3, 516–524.[MR]
  69. Tim Dokchitser and Vladimir Dokchitser, A note on the Mordell-Weil rank modulo n, preprint (2009), 7 pages.[arXiv]
  70. Darrin Doud, A procedure to calculate torsion of elliptic curves over Q, Manuscripta Math. 95 (1998), no. 4, 463–469.[MR]
  71. Andrej Dujella, On Mordell-Weil groups of elliptic curves induced by Diophantine triples, Glas. Mat. Ser. III 42(62) (2007), no. 1, 3–18.[MR/arXiv]
  72. S. Duquesne, Rational points on hyperelliptic curves and an explicit Weierstrass preparation theorem, Manuscripta Math. 108 (2002), no. 2, 191–204.[MR]
  73. Sylvain Duquesne, Points rationnels et méthode de Chabauty elliptique, J. Théor. Nombres Bordeaux 15 (2003), no. 1, 99–113.[MR]
  74. Sylvain Duquesne, Elliptic curves associated with simplest quartic fields, J. Théor. Nombres Bordeaux 19 (2007), no. 1, 81–100.[MR]
  75. Sylvain Duquesne, Montgomery ladder for all genus 2 curves in characteristic 2, Arithmetic of Finite Fields, Lecture Notes in Computer Science, vol. 5130, Springer, 2008, pp. 174–188.
  76. Sylvain Duquesne, Traces of the group law on the Kummer surface of a curve of genus 2 in characteristic 2, Math. Comput. Sci. 3 (2010), no. 2, 173–183.
  77. Bas Edixhoven, On the computation of the coefficients of a modular form, Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 30–39.[MR]
  78. Kirsten Eisentraeger, Dimitar Jetchev, and Kristin Lauter, On the computation of the Cassels pairing for certain Kolyvagin classes in the Shafarevich-Tate group, preprint 5209 (2008), 113–125.
  79. Kirsten Eisenträger and Kristin Lauter, A CRT algorithm for constructing genus 2 curves over finite fields, preprint (2007), 16 pages.[arXiv]
  80. Noam D. Elkies, Three lectures on elliptic surfaces and curves of high rank, preprint (2007), 14 pages.[arXiv]
  81. Noam D. Elkies, Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, Springer, 2008, pp. 196-211.[arXiv]
  82. Noam D. Elkies and Mark Watkins, Elliptic curves of large rank and small conductor, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 3076, Springer, Berlin, 2004, pp. 42–56.[MR]
  83. Arsen Elkin, Hyperelliptic Jacobians with real multiplication, J. Number Theory 117 (2006), no. 1, 53–86.[MR]
  84. Andreas-Stephan Elsenhans and Jörg Jahnel, K3 surfaces of Picard rank one and degree two, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, Springer, 2008, pp. 212–225.
  85. G. Everest and T. Ward, The canonical height of an algebraic point on an elliptic curve, New York J. Math. 6 (2000), 331–342 (electronic).[MR]
  86. Graham Everest, Patrick Ingram, Valéry Mahé, and Shaun Stevens, The uniform primality conjecture for elliptic curves, Acta Arith. 134 (2008), no. 2, 157–181.[MR/arXiv]
  87. Graham Everest, Patrick Ingram, and Shaun Stevens, Primitive divisors on twists of Fermat's cubic, LMS J. Comput. Math. 12 (2009), 54–81.[MR/arXiv]
  88. Graham Everest and Valéry Mahé, A generalization of Siegel's theorem and Hall's conjecture, Experiment. Math. 18 (2009), no. 1, 1–9.[MR/arXiv]
  89. Graham Everest, Ouamporn Phuksuwan, and Shaun Stevens, The uniform primality conjecture for the twisted Fermat cubic, preprint (2010), 21 pages.[arXiv]
  90. Xander Faber and Benjamin Hutz, On the number of rational iterated pre-images of the origin under quadratic dynamical systems, preprint (2008), 18 pages.[arXiv]
  91. Reza Rezaeian Farashahi and Ruud Pellikaan, The quadratic extension extractor for (hyper)elliptic curves in odd characteristic, Arithmetic of finite fields, Lecture Notes in Comput. Sci., vol. 4547, Springer, Berlin, 2007, pp. 219–236.[MR]
  92. Luca De Feo, Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic, J. Number Theory, to appear (2010), 21 pages.[arXiv]
  93. Julio Fernández, Josep González, and Joan-C. Lario, Plane quartic twists of X(5,3), Canad. Math. Bull. 50 (2007), no. 2, 196–205.[MR]
  94. Luís R. A. Finotti, Degrees of the elliptic Teichmüller lift, J. Number Theory 95 (2002), no. 2, 123–141.[MR]
  95. Luís R. A. Finotti, Minimal degree liftings of hyperelliptic curves, J. Math. Sci. Univ. Tokyo 11 (2004), no. 1, 1–47.[MR]
  96. Luís R. A. Finotti, Minimal degree liftings in characteristic 2, J. Pure Appl. Algebra 207 (2006), no. 3, 631–673.[MR]
  97. Luís R. A. Finotti, Lifting the j-invariant: Questions of Mazur and Tate, J. Number Theory 130 (2010), no. 3, 620–638.[doi]
  98. Tom Fisher, Testing equivalence of ternary cubics, Algorithmic Number Theory (Berlin, 2006), Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 333–345.[MR]
  99. Tom Fisher, The Hessian of a genus one curve, preprint (2006), 28 pages.[arXiv]
  100. Tom Fisher, A new approach to minimising binary quartics and ternary cubics, Math. Res. Lett. 14 (2007), no. 4, 597–613.[MR/link]
  101. Tom Fisher, Some improvements to 4-descent on an elliptic curve, Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 5011, Springer, Berlin, 2008, pp. 125–138.[MR/doi]
  102. Tom Fisher, The invariants of a genus one curve, Proc. Lond. Math. Soc. (3) 97 (2008), no. 3, 753–782.[MR/arXiv]
  103. E. V. Flynn, The Hasse principle and the Brauer-Manin obstruction for curves, Manuscripta Math. 115 (2004), no. 4, 437–466.[MR]
  104. E. V. Flynn and C. Grattoni, Descent via isogeny on elliptic curves with large rational torsion subgroups, J. Symbolic Comput. 43 (2008), no. 4, 293–303.[MR]
  105. E. V. Flynn and J. Wunderle, Cycles of covers, Monatsh. Math. Online first (2008), 16.
  106. David Freeman, Peter Stevenhagen, and Marco Streng, Abelian varieties with prescribed embedding degree, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, Springer, 2008, pp. 60-73.[arXiv]
  107. S. D. Galbraith, J. F. McKee, and P. C. Valença, Ordinary abelian varieties having small embedding degree, Finite Fields Appl. 13 (2007), no. 4, 800–814.[MR]
  108. Steven D. Galbraith, Weil descent of Jacobians, Discrete Appl. Math. 128 (2003), no. 1, 165–180.[MR]
  109. Irene García-Selfa, Enrique González-Jiménez, and José M. Tornero, Galois theory, discriminants and torsion subgroup of elliptic curves, J. Pure Appl. Algebra 214 (2010), no. 8, 1340–1346.[MR/doi]
  110. P. Gaudry and É. Schost, Modular equations for hyperelliptic curves, Math. Comp. 74 (2005), no. 249, 429–454 (electronic).[MR]
  111. Pierrick Gaudry, Index calculus for abelian varieties and the elliptic curve discrete logarithm problem, Preprint (2004), 13 pages.
  112. Pierrick Gaudry and Robert Harley, Counting points on hyperelliptic curves over finite fields, Algorithmic Number Theory (Leiden, 2000), Lecture Notes in Comput. Sci., vol. 1838, Springer, Berlin, 2000, pp. 313–332.[MR]
  113. Eknath Ghate, Enrique González-Jiménez, and Jordi Quer, On the Brauer class of modular endomorphism algebras, Int. Math. Res. Not. (2005), no. 12, 701–723.[MR]
  114. Jean Gillibert, Invariants de classes: exemples de non-annulation en dimension supérieure, Math. Ann. 338 (2007), no. 2, 475–495.[MR]
  115. Edray Goins, Explicit descent via 4-isogeny on an elliptic curve, preprint (2004), 20 pages.[arXiv]
  116. Josep González and Jordi Guàrdia, Genus two curves with quaternionic multiplication and modular Jacobian, Math. Comp. 78 (2009), no. 265, 575–589.[MR]
  117. Josep González, Jordi Guàrdia, and Victor Rotger, Abelian surfaces of GL2-type as Jacobians of curves, Acta Arith. 116 (2005), no. 3, 263–287.[MR]
  118. Josep González and Victor Rotger, Non-elliptic Shimura curves of genus one, J. Math. Soc. Japan 58 (2006), no. 4, 927–948.[MR]
  119. Enrique González-Jiménez, Josep González, and Jordi Guàrdia, Computations on modular Jacobian surfaces, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 189–197.[MR]
  120. Enrique González-Jiménez and Roger Oyono, Non-hyperelliptic modular curves of genus 3, J. Number Theory 130 (2010), no. 4, 862–878.[MR/doi]
  121. Enrique Gonzalez-Jimenez and Xavier Xarles, Five squares in arithmetic progression over quadratic fields, preprint (2009), 24 pages.[arXiv]
  122. Enrique Gonzalez-Jimenez and Xavier Xarles, On symmetric square values of quadratic polynomials, preprint (2010).[arXiv]
  123. Eyal Z. Goren and Kristin E. Lauter, The distance between superspecial abelian varieties with real multiplication, J. Number Theory 129 (2009), no. 6, 1562–1578.[MR]
  124. Eyal Z. Goren and Kristin E. Lauter, Genus 2 curves with complex multiplication, preprint (2010).[arXiv]
  125. Matthew Greenberg, Computing Heegner points arising from Shimura curve parametrizations, Preprint (2006), 11 pages.[link]
  126. Matthew Greenberg, Heegner Points and Rigid Analytic Modular Forms, PhD Thesis, McGill University, 2006.[link]
  127. Matthew Greenberg, Heegner point computations via numerical p-adic integration, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 4076, Springer Berlin / Heidelberg, 2006, pp. 361–376.[link]
  128. Grigor Grigorov, Andrei Jorza, Stephan Patrikis, William A. Stein, and Corina Tarnita-Patrascu, Verification of the Birch and Swinnerton-Dyer conjecture for specific elliptic curves, Preprint, 26 pages.
  129. Jordi Guàrdia, Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves, Ann. Inst. Fourier (Grenoble) 57 (2007), no. 4, 1253–1283.[MR]
  130. Brian Hansen, Explicit computations supporting a generalization of Serre's conjecture, Master's Thesis, Brigham Young University, 2005.
  131. Robin Hartshorne and Ronald van Luijk, Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces, Math. Intelligencer 30 (2008), no. 4, 4–10.[MR/arXiv]
  132. Ki-ichiro Hashimoto, Katsuya Miyake, and Hiroaki Nakamura (eds.), Galois Theory and Modular Forms, in Proceedings of the International Conference held at Tokyo Metropolitan University, Tokyo, September 25–29, 2001, Developments in Mathematics, vol. 11, Kluwer Academic Publishers, Boston, MA, 2004, pp. xii+393.[MR]
  133. Brendan Hassett, Anthony Vàrilly-Alvarado, and Patrick Varilly, Transcendental obstructions to weak approximation on general K3 surfaces, preprint (2010), 24 pages.[arXiv]
  134. Florian Hess, Computing relations in divisor class groups of algebraic curves over finite fields, Preprint (2003).
  135. Florian Hess, A note on the Tate pairing of curves over finite fields, Arch. Math. (Basel) 82 (2004), no. 1, 28–32.[MR]
  136. Laura Hitt, Families of genus 2 curves with small embedding degree, J. Math. Cryptol. 3 (2009), no. 1, 19–36.[MR/link]
  137. E. W. Howe and K. E. Lauter, Improved upper bounds for the number of points on curves over finite fields, Ann. Inst. Fourier (Grenoble) 53 (2003), no. 6, 1677–1737.[MR]
  138. Everett W. Howe, Infinite families of pairs of curves over Q with isomorphic Jacobians, J. London Math. Soc. (2) 72 (2005), no. 2, 327–350.[MR]
  139. Everett W. Howe, Supersingular genus-2 curves over fields of characteristic 3, Computational arithmetic geometry, Contemp. Math., vol. 463, Amer. Math. Soc., Providence, RI, 2008, pp. 49–69.[MR/arXiv]
  140. Everett W. Howe, Kristin E. Lauter, and Jaap Top, Pointless curves of genus three and four, Arithmetic, Geometry and Coding Theory (AGCT 2003), Sémin. Congr., vol. 11, Soc. Math. France, Paris, 2005, pp. 125–141.[MR]
  141. Everett W. Howe and Hui June Zhu, On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field, J. Number Theory 92 (2002), no. 1, 139–163.[MR]
  142. Hendrik Hubrechts, Point counting in families of hyperelliptic curves, Found. Comput. Math. 8 (2008), no. 1, 137–169.[MR/arXiv]
  143. Hendrik Hubrechts, Quasi-quadratic elliptic curve point counting using rigid cohomology, J. Symb. Comput. 44 (2009), no. 9, 1255–1267.[arXiv]
  144. Klaus Hulek and Helena Verrill, On modularity of rigid and nonrigid Calabi-Yau varieties associated to the root lattice A4, Nagoya Math. J. 179 (2005), 103–146.[MR]
  145. Klaus Hulek and Helena A. Verrill, On the motive of Kummer varieties associated to Γ1(7)— Supplement to the paper: "The modularity of certain non-rigid Calabi-Yau threefolds" by R. Livné and N. Yui, J. Math. Kyoto Univ. 45 (2005), no. 4, 667–681.[MR/link]
  146. Patrick Ingram, Multiples of integral points on elliptic curves, J. Number Theory 129 (2009), no. 1, 182–208.[MR/doi]
  147. Farzali A. Izadi and V. Kumar Murty, Counting points on an abelian variety over a finite field, Progress in Cryptology—Indocrypt 2003, Lecture Notes in Comput. Sci., vol. 2904, Springer, Berlin, 2003, pp. 323–333.[MR]
  148. David Jao and Vladimir Soukharev, A subexponential algorithm for evaluating large degree isogenies, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 6197, Springer, Berlin, 2010, pp. 219–233.[doi/arXiv]
  149. Dimitar Jetchev, Kristin Lauter, and William Stein, Explicit Heegner points: Kolyvagin's conjecture and non-trivial elements in the Shafarevich-Tate group, J. Number Theory 129 (2009), no. 2, 284–302.[doi]
  150. Dimitar P. Jetchev and William A. Stein, Visibility of the Shafarevich-Tate group at higher level, Doc. Math. 12 (2007), 673–696.[MR]
  151. Jorge Jimenez-Urroz and Tonghai Yang, Heegner zeros of theta functions, Trans. Amer. Math. Soc. 355 (2003), no. 10, 4137–4149 (electronic).[MR]
  152. Rafe Jones and Jeremy Rouse, Galois theory of iterated endomorphisms, Proc. London Math. Soc. (3) 100 (2010), 763–794.[doi]
  153. David Joyner and Amy Ksir, Modular representations on some Riemann-Roch spaces of modular curves X(N), Computational Aspects of Algebraic Curves, Lecture Notes Ser. Comput., vol. 13, World Sci. Publ., Hackensack, NJ, 2005, pp. 163–205.[MR]
  154. Ben Kane, CM liftings of supersingular elliptic curves, preprint (2009), 26 pages.[arXiv]
  155. Koray Karabina and Edlyn Teske, On prime-order elliptic curves with embedding degrees k=3,4, and 6, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, Springer, 2008, pp. 102–117.
  156. L. J. P. Kilford, Some non-Gorenstein Hecke algebras attached to spaces of modular forms, J. Number Theory 97 (2002), no. 1, 157–164.[MR]
  157. L. J. P. Kilford, Slopes of 2-adic overconvergent modular forms with small level, Math. Res. Lett. 11 (2004), no. 5-6, 723–739.[MR]
  158. L. J. P. Kilford, On a p-adic extension of the Jacquet-Langlands correspondence to weight 1, preprint (2008), 17 pages.[arXiv]
  159. David R. Kohel, Hecke module structure of quaternions, Class Field Theory—Its Centenary and Prospect (Tokyo, 1998), Adv. Stud. Pure Math., vol. 30, Math. Soc. Japan, Tokyo, 2001, pp. 177–195.[MR]
  160. David R. Kohel, The AGM-X0(N) Heegner point lifting algorithm and elliptic curve point counting, Advances in Cryptology—Asiacrypt 2003, Lecture Notes in Comput. Sci., vol. 2894, Springer, Berlin, 2003, pp. 124–136.[MR]
  161. David R. Kohel and William A. Stein, Component groups of quotients of J0(N), Algorithmic Number Theory (Leiden, 2000), Lecture Notes in Comput. Sci., vol. 1838, Springer, Berlin, 2000, pp. 405–412.[MR]
  162. David R. Kohel and Helena A. Verrill, Fundamental domains for Shimura curves, J. Théor. Nombres Bordeaux 15 (2003), no. 1, 205–222.[MR]
  163. Kenji Koike and Annegret Weng, Construction of CM Picard curves, Math. Comp. 74 (2005), no. 249, 499–518 (electronic).[MR]
  164. Aristides Kontogeorgis and Victor Rotger, On the non-existence of exceptional automorphisms on Shimura curves, Bull. Lond. Math. Soc. 40 (2008), no. 3, 363–374.[MR/arXiv]
  165. Andrew Kresch and Yuri Tschinkel, Integral points on punctured abelian surfaces, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 198–204.[MR]
  166. L. Kulesz, G. Matera, and É. Schost, Uniform bounds on the number of rational points of a family of curves of genus 2, J. Number Theory 108 (2004), no. 2, 241–267.[MR]
  167. Dominic Lanphier, The trace of special values of modular L-functions, Preprint, 18 pages.
  168. Alan G. B. Lauder, Ranks of elliptic curves over function fields, LMS J. Comput. Math. 11 (2008), 172–212.[MR]
  169. Alan G. B. Lauder, Degenerations and limit Frobenius structures in rigid cohomology, preprint (2009), 41 pages.[arXiv]
  170. F. Leprévost, M. Pohst, and A. Schöpp, Rational torsion of J0(N) for hyperelliptic modular curves and families of Jacobians of genus 2 and genus 3 curves with a rational point of order 5, 7 or 10, Abh. Math. Sem. Univ. Hamburg 74 (2004), 193–203.[MR]
  171. Franck Leprévost, Michael Pohst, and Andreas Schöpp, Familles de polynômes liées aux courbes modulaires X(l) unicursales et points rationnels non-triviaux de courbes elliptiques quotient, Acta Arith. 110 (2003), no. 4, 401–410.[MR]
  172. Reynald Lercier and David Lubicz, A quasi-quadratic time algorithm for hyperelliptic curve point counting, Ramanujan J. 12 (2006), no. 3, 399–423.[MR/doi]
  173. Reynald Lercier and Thomas Sirvent, On Elkies subgroups of l-torsion points in elliptic curves defined over a finite field, J. Théor. Nombres Bordeaux 20 (2008), no. 3, 783–797.[MR/arXiv]
  174. Petr Lisoněk, On the connection between Kloosterman sums and elliptic curves, Sequences and Their Applications – SETA 2008: Proceedings, Lecture Notes in Computer Science, vol. 5203, Springer, Berlin Heidelberg, 2008, pp. 182–187.
  175. Adam Logan and Ronald van Luijk, Nontrivial elements of Sha explained through K3 surfaces, Math. Comp. 78 (2009), no. 265, 441–483.[MR]
  176. Ling Long and Chris Kurth, On modular forms for some noncongruence subgroups of SL2Z) II, preprint (2008), 13 pages.[arXiv]
  177. Dino Lorenzini and Thomas J. Tucker, Thue equations and the method of Coleman-Chabauty, preprint (2000), 30 pages.[arXiv]
  178. Álvaro Lozano-Robledo, On the product of twists of rank two and a conjecture of Larsen, Ramanujan J. 19 (2009), no. 1, 53–61.[MR/doi]
  179. Kazuo Matsuno, Construction of elliptic curves with large Iwasawa λ-invariants and large Tate-Shafarevich groups, Manuscripta Math. 122 (2007), no. 3, 289–304.[MR]
  180. Kazuto Matsuo, Jinhui Chao, and Shigeo Tsujii, An improved baby step giant step algorithm for point counting of hyperelliptic curves over finite fields, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 461–474.[MR]
  181. J. Miret, R. Moreno, A. Rio, and M. Valls, Computing the l-power torsion of an elliptic curve over a finite field, Math. Comp. 78 (2009), no. 267, 1767–1786.[MR]
  182. J. Miret, R. Moreno, D. Sadornil, J. Tena, and M. Valls, Computing the height of volcanoes of l-isogenies of elliptic curves over finite fields, Appl. Math. Comput. 196 (2008), no. 1, 67–76.[MR]
  183. Josep M. Miret, Jordi Pujolàs, and Anna Rio, Bisection for genus 2 curves in odd characteristic, Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), no. 4, 55–60.[MR/doi]
  184. Jan-Steffen Müller, Explicit Kummer surface theory for arbitrary characteristic, London Math. Soc. J. Comput. Math. 13 (2010), 47–64.[arXiv]
  185. Filip Najman, Complete classification of torsion of elliptic curves over quadratic cyclotomic fields, J. Number Theory 130 (2010), no. 9, 1964–1968.[MR/doi]
  186. Annika Niehage, Quantum Goppa codes over hypereliptic curves, Master's Thesis, Universität Mannheim, 2004.
  187. Ekin Ozman, Local points on quadratic twists of X0(N), preprint (2009), 26 pages.[arXiv]
  188. Mihran Papikian, On the degree of modular parametrizations over function fields, J. Number Theory 97 (2002), no. 2, 317–349.[MR/doi]
  189. Mihran Papikian, On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves, J. Number Theory 115 (2005), no. 2, 249–283.[MR]
  190. Bernadette Perrin-Riou, Arithmétique des courbes elliptiques à réduction supersingulière en p, Experiment. Math. 12 (2003), no. 2, 155–186.[MR/link]
  191. Bjorn Poonen, Computational aspects of curves of genus at least 2, Algorithmic Number Theory (Talence, 1996), Lecture Notes in Comput. Sci., vol. 1122, Springer, Berlin, 1996, pp. 283–306.[MR]
  192. Bjorn Poonen, Edward F. Schaefer, and Michael Stoll, Twists of X(7) and primitive solutions to x2+y3=z7, Duke Math. J. 137 (2007), no. 1, 103–158.[MR]
  193. Lisa Marie Redekop, Torsion Points of Low Order on Elliptic Curves and Drinfeld Modules, PhD Thesis, 2002.[link]
  194. Jonathan Reynolds, Extending Siegel's theorem for elliptic curves, PhD Thesis, University of East Anglia, 2008.[link]
  195. Guillaume Ricotta and Thomas Vidick, Hauteur asymptotique des points de Heegner, Canad. J. Math. 60 (2008), no. 6, 1406–1436.[MR]
  196. Christophe Ritzenthaler, Automorphismes des courbes modulaires X(n) en caractéristique p, Manuscripta Math. 109 (2002), no. 1, 49–62.[MR]
  197. Christophe Ritzenthaler, Point counting on genus 3 non hyperelliptic curves, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 3076, Springer, Berlin, 2004, pp. 379–394.[MR]
  198. Christophe Ritzenthaler, Explicit computations of Serre's obstruction for genus 3 curves and application to optimal curves, LMS Journal of Computation and Mathematics 13 (2010), 192–207.[arXiv]
  199. Mohammad Sadek, Counting models of genus one curves, preprint (2010), 22 pages.[arXiv]
  200. David Savitt, The maximum number of points on a curve of genus 4 over F8 is 25, Canad. J. Math. 55 (2003), no. 2, 331–352.[MR]
  201. Edward F. Schaefer and Michael Stoll, How to do a p-descent on an elliptic curve, Trans. Amer. Math. Soc. 356 (2004), no. 3, 1209–1231 (electronic).[MR]
  202. Jasper Scholten, Weil restriction of an elliptic curve over a quadratic extension, Preprint (2004), 6 pages.
  203. Andreas M. Schöpp, Über torsionspunkte elliptischer und hyperelliptischer kurven nebst anwendungen, PhD Thesis, Technische Universitaet Berlin,, 2005.
  204. Samir Siksek, On standardized models of isogenous elliptic curves, Math. Comp. 74 (2005), no. 250, 949–951 (electronic).[MR]
  205. Samir Siksek, Chabauty for symmetric powers of curves, Algebra Number Theory 3 (2009), no. 2, 209–236.[MR/doi]
  206. Samir Siksek and John E. Cremona, On the Diophantine equation x2+7=ym, Acta Arith. 109 (2003), no. 2, 143–149.[MR]
  207. Samir Siksek and Michael Stoll, On a problem of Hajdu and Tengely, preprint (2009), 8 pages.[arXiv]
  208. Benjamin Smith, Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves, Advances in Cryptology, Eurocrypt 2008, Lecture Notes in Computer Science, vol. 4965, Springer Berlin/Heidelberg, 2008, pp. 163–180.[eprint]
  209. Benjamin Smith, Families of explicit isogenies of hyperelliptic Jacobians, Arithmetic, Geometry, Cryptography and Coding Theory, Contemporary Mathematics, vol. 521, AMS, Providence, R.I., 2009, pp. 121–144.[arXiv]
  210. Sebastian Karl Michael Stamminger, Explicit 8-descent on elliptic curves, PhD Thesis, International University Bremen, 2005.
  211. William A. Stein, There are genus one curves over Q of every odd index, J. Reine Angew. Math. 547 (2002), 139–147.[MR]
  212. William A. Stein, Shafarevich-Tate groups of nonsquare order, Modular curves and abelian varieties, Progr. Math., vol. 224, Birkhäuser, Basel, 2004, pp. 277–289.[MR]
  213. William Stein, Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 93–116.[MR]
  214. William A. Stein, Visibility of Mordell-Weil groups, Doc. Math. 12 (2007), 587–606.[MR]
  215. Michael Stoll, Implementing 2-descent for Jacobians of hyperelliptic curves, Acta Arith. 98 (2001), no. 3, 245–277.[MR]
  216. Michael Stoll, On the height constant for curves of genus two. II, Acta Arith. 104 (2002), no. 2, 165–182.[MR]
  217. Michael Stoll, Rational 6-cycles under iteration of quadratic polynomials, LMS J. Comput. Math. 11 (2008), 367–380.[arXiv]
  218. Fritz Grunewald Tatiana Bandman, Shelly Garion, On the surjectivity of engel words on psl(2,q), preprint (2010), 1–22.[arXiv]
  219. Thotsaphon Thongjunthug, Computing a lower bound for the canonical height on elliptic curves over totally real number fields, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, Springer, 2008, pp. 139-152.
  220. Anthony Vàrilly-Alvarado and Bianca Viray, Failure of the Hasse principle for Enriques surfaces, Advances in Mathematics 226 (2011), 4884–4901.[arXiv]
  221. Marie-France Vignéras, p-adic integral structures of some representations of GL(2, F), Preprint (2005), 23 pages.[link]
  222. Bogdan G. Vioreanu, Mordell-Weil problem for cubic surfaces, numerical evidence, preprint (2008), 22 pages.[arXiv]
  223. Bianca Viray, A family of varieties with exactly one pointless rational fiber, preprint (2009), 4 pages.[arXiv]
  224. Mark Watkins, A note on integral points on elliptic curves, J. Théor. Nombres Bordeaux 18 (2006), no. 3, 707–720.[MR]
  225. Mark Watkins, Some remarks on Heegner point computations, preprint (2006), 14 pages.[arXiv]
  226. Mark Watkins, Some heuristics about elliptic curves, Experiment. Math. 17 (2008), no. 1, 105–125.[MR/arXiv]
  227. Rolf Stefan Wilke, On rational embeddings of curves in the second Garcia-Stichtenoth tower, Finite Fields Appl. 14 (2008), no. 2, 494–504.[MR]
  228. Christian Wuthrich, Self-points on an elliptic curve of conductor 14, in Proceedings of the Symposium on Algebraic Number Theory and Related Topics, RIMS Kôkyûroku Bessatsu, B4, Res. Inst. Math. Sci. (RIMS), Kyoto, 2007, pp. 189–195.[MR]
  229. Christian Wuthrich, The fine Tate-Shafarevich group, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 1–12.[MR]
  230. Chaoping Xing, Applications of algebraic curves to constructions of sequences, Cryptography and Computational Number Theory (Singapore, 1999), Progr. Comput. Sci. Appl. Logic, vol. 20, Birkhäuser, Basel, 2001, pp. 137–146.[MR]
  231. Chaoping Xing and Sze Ling Yeo, Construction of global function fields from linear codes and vice versa, Trans. Amer. Math. Soc. 361 (2008), no. 3, 1333-1349.
  232. Huilin Zhu and Jianhua Chen, Integral points on a class of elliptic curve, Wuhan Univ. J. Nat. Sci. 11 (2006), no. 3, 477–480.[MR]