Number Theory

1. Kanat Abdukhalikov, Unimodular Hermitian lattices, Mathematisches Forschungsinstitut Oberwolfach Report No. 1/2005 (2005), 27–30.
2. Kanat Abdukhalikov and Rudolf Scharlau, Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers, Math. Comp. 78 (2009), no. 265, 387–403.^[MR]
3. Fadwa S. Abu Muriefah, Florian Luca, and Alain Togbé, On the Diophantine equation x²+5^a13^b=yⁿ, Glasg. Math. J. 50 (2008), no. 1, 175–181.^[MR]
4. Fatima K. Abu Salem and Kamal Khuri-Makdisi, Fast Jacobian group operations for C_3,4 curves over a large finite field, LMS J. Comput. Math. 10 (2007), 307–328 (electronic).^[MR]
5. Amod Agashe, Kenneth Ribet, and William A. Stein, The Manin constant, Pure Appl. Math. Q. 2 (2006), no. 2, 617–636.^[MR]
6. Amod Agashe and William Stein, Visibility of Shafarevich-Tate groups of abelian varieties, J. Number Theory 97 (2002), no. 1, 171–185.^[MR]
7. 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]
8. Scott Ahlgren, On the irreducibility of Hecke polynomials, Math. Comp. 77 (2008), no. 263, 1725–1731.^[MR]
9. Scott Ahlgren and Ken Ono, Arithmetic of singular moduli and class polynomials, Compos. Math. 141 (2005), no. 2, 293–312.^[MR]
10. Scott Ahlgren and Matthew Papanikolas, Higher Weierstrass points on X₀(p), Trans. Amer. Math. Soc. 355 (2003), no. 4, 1521–1535 (electronic).^[MR]
11. Ali Akhavi and Damien Stehlé, Speeding-up lattice reduction with random projections (extended abstract), LATIN 2008: Theoretical informatics, Lecture Notes in Comput. Sci., vol. 4957, Springer, Berlin, 2008, pp. 293–305.^[MR]
12. S. Akhtari, A. Togbé, and P. G. Walsh, On the equation aX⁴-bY² = 2, Acta Arith. 131 (2008), no. 2, 145–169.^[MR]
13. Shabnam Akhtari, The diophantine equation aX⁴ – bY² = 1, Journal fur die Reine und Angewandte Mathematik, to appear (2009), 20 pages.^[arXiv]
14. Shabnam Akhtari, The method of Thue-Siegel for binary quartic forms, preprint (2009), 35 pages.^[arXiv]
15. Bill Allombert, An efficient algorithm for the computation of Galois automorphisms, Math. Comp. 73 (2004), no. 245, 359–375 (electronic).^[MR]
16. Avner Ash, Jos Brakenhoff, and Theodore Zarrabi, Equality of polynomial and field discriminants, Experiment. Math. 16 (2007), no. 3, 367–374.^[MR/link]
17. 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]
18. A. O. L. Atkin, Wen-Ching Winnie Li, and Ling Long, On Atkin and Swinnerton-Dyer congruence relations (II), Math. Ann. 340 (2008), no. 2, 335–358.^[MR/arXiv]
19. Roberto Maria Avanzi, Another look at square roots (and other less common operations) in fields of even characteristic, Selected Areas in Cryptography, Lecture Notes in Computer Science, vol. 4876/2007, Springer Berlin / Heidelberg, 2007, pp. 138–154.^[eprint]
20. Huseyin Aydin, Ramazan Dikici, and Geoff C. Smith, Wall and Vinson revisited, Applications of Fibonacci Numbers, Vol. 5 (St. Andrews, 1992), Kluwer Acad. Publ., Dordrecht, 1993, pp. 61–68.^[MR]
21. Eric Bach and Denis Charles, The hardness of computing an eigenform, Computational arithmetic geometry, Contemp. Math., vol. 463, Amer. Math. Soc., Providence, RI, 2008, pp. 9–15.^[MR/arXiv]
22. Christine Bachoc and Gabriele Nebe, Classification of two genera of 32-dimensional lattices of rank 8 over the Hurwitz order, Experiment. Math. 6 (1997), no. 2, 151–162.^[MR]
23. Christine Bachoc and Boris Venkov, Modular forms, lattices and spherical designs, Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, Monogr. Enseign. Math., vol. 37, Enseignement Math., Geneva, 2001, pp. 87–111.^[MR]
24. Werner Backes and Susanne Wetzel, Heuristics on lattice basis reduction in practice, ACM J. Exp. Algorithmics 7 (2002), 21 pp. (electronic).^[MR]
25. Werner Backes and Susanne Wetzel, An efficient LLL gram using buffered transformations, Computer Algebra in Scientific Computing, Lecture Notes in Computer Science, vol. 4770/2007, Springer Berlin / Heidelberg, 2007, pp. 31–44.
26. David H. Bailey and Jonathan M. Borwein, Experimental mathematics: Examples, methods and implications, Notices Amer. Math. Soc. 52 (2005), no. 5, 502–514.^[MR]
27. David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor, and Eric W. Weisstein, Ten problems in experimental mathematics, Amer. Math. Monthly 113 (2006), no. 6, 481–509.^[MR]
28. 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]
29. R. D. Baker, G. L. Ebert, K. H. Leung, and Q. Xiang, A trace conjecture and flag-transitive affine planes, J. Combin. Theory Ser. A 95 (2001), no. 1, 158–168.^[MR]
30. Stéphane Ballet, Quasi-optimal algorithms for multiplication in the extensions of \bf F₁₆ of degree 13, 14 and 15, J. Pure Appl. Algebra 171 (2002), no. 2-3, 149–164.^[MR]
31. 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]
32. Laurent Bartholdi and Michael R. Bush, Maximal unramified 3-extensions of imaginary quadratic fields and SL₂(Z₃), J. Number Theory 124 (2007), no. 1, 159–166.^[MR/arXiv]
33. Ingrid Bauer, Fabrizio Catanese, and Fritz Grunewald, The absolute Galois group acts faithfully on the connected components of the moduli space of surfaces of general type, preprint (2007), 13 pages.^[arXiv]
34. M. Bauer, M. J. Jacobson, Jr., Y. Lee, and R. Scheidler, Construction of hyperelliptic function fields of high three-rank, Math. Comp. 77 (2008), no. 261, 503–530 (electronic).^[MR]
35. 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]
36. Michael Beck, Eric Pine, Wayne Tarrant, and Kim Yarbrough Jensen, New integer representations as the sum of three cubes, Math. Comp. 76 (2007), no. 259, 1683–1690 (electronic).^[MR]
37. M. A. Bennett, N. Bruin, K. Győry, and L. Hajdu, Powers from products of consecutive terms in arithmetic progression, Proc. London Math. Soc. (3) 92 (2006), no. 2, 273–306.^[MR]
38. Michael A. Bennett, The Diophantine equation (x^k-1)(y^k-1)=(z^k-1)^t, Indag. Math. (N.S.) 18 (2007), no. 4, 507–525.^[MR]
39. Michael A. Bennett, Kálmán Győry, and Ákos Pintér, On the Diophantine equation 1^k+2^k+.s+x^k=yⁿ, Compos. Math. 140 (2004), no. 6, 1417–1431.^[MR]
40. A. Bérczes, A. Pethő, and V. Ziegler, Parameterized norm form equations with arithmetic progressions, J. Symbolic Comput. 41 (2006), no. 7, 790–810.^[MR]
41. Attila Bérczes and Attila Pethő, Computational experiences on norm form equations with solutions forming arithmetic progressions, Glas. Mat. Ser. III 41(61) (2006), no. 1, 1–8.^[MR]
42. Tobias Berger, An Eisenstein ideal for imaginary quadratic fields and the Bloch-Kato conjecture for Hecke characters, preprint (2007), 26 pages.^[arXiv]
43. 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]
44. Tobias Berger and Krzysztof Klosin, A deformation problem for Galois representations over imaginary quadratic fields, J. Inst. Math. Jussieu, to appear (2009), 19.
45. Alexander Berkovich and William C. Jagy, Ternary quadratic forms, modular equations and certain positivity conjectures, The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, Springer, New York, 2009, pp. 211–241.^[doi]
46. Daniel J. Bernstein, Batch binary edwards, Advances in Cryptology - CRYPTO 2009, Lecture Notes in Comput. Sci., vol. 5677, Springer, Berlin, 2009, pp. 317–336.^[doi]
47. Daniel J. Bernstein, Peter Birkner, Tanja Lange, and Christiane Peters, Optimizing double-base elliptic-curve single-scalar multiplication, Progress in cryptology—INDOCRYPT 2007, Lecture Notes in Comput. Sci., vol. 4859, Springer, Berlin, 2007, pp. 167–182.^[MR/doi]
48. Daniel J. Bernstein, Peter Birkner, Tanja Lange, and Christiane Peters, ECM using Edwards curves, IACR (2008), 18 pages.^[eprint]
49. Daniel J. Bernstein and Tanja Lange, Faster addition and doubling on elliptic curves, Advances in Cryptology - ASIACRYPT 2007, Lecture Notes in Computer Science, vol. 4833/2007, Springer Berlin / Heidelberg, 2007, pp. 29–50.
50. 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]
51. Manjul Bhargava, Higher composition laws I: A new view on Gauss composition, and quadratic generalizations, Ann. of Math. (2) 159 (2004), no. 1, 217–250.^[MR]
52. Peter Birkner, Efficient arithmetic on low-genus curves, PhD Thesis, Technische Universiteit Eindhoven, 2009.
53. Peter Birkner, Efficient divisor class halving on genus two curves, Selected Areas in Cryptography, Lecture Notes in Computer Science, vol. 4356, Springer, Berlin/Heidelberg, pp. 317–326.^[link]
54. Werner Bley and Robert Boltje, Computation of locally free class groups, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 72–86.^[MR/link]
55. Aart Blokhuis, Robert S. Coulter, Marie Henderson, and Christine M. O'Keefe, Permutations amongst the Dembowski-Ostrom polynomials, Finite fields and applications (Augsburg, 1999), Springer, Berlin, 2001, pp. 37–42.^[MR]
56. Siegfried Boecherer and Gabriele Nebe, On theta series attached to maximal lattices and their adjoints, preprint (2009), 16 pages.^[arXiv]
57. Jonathan Borwein and David Bailey, Mathematics by Experiment, A K Peters Ltd., Natick, MA, 2004, pp. x+288.^[MR]
58. Peter Borwein, Greg Fee, Ron Ferguson, and Alexa van der Waall, Zeros of partial sums of the Riemann zeta function, Experiment. Math. 16 (2007), no. 1, 21–39.^[MR/link]
59. Wieb Bosma, Canonical bases for cyclotomic fields, Appl. Algebra Engrg. Comm. Comput. 1 (1990), no. 2, 125–134.^[MR]
60. Wieb Bosma, Explicit primality criteria for h·2^k±1, Math. Comp. 61 (1993), no. 203, 97–109.^[MR]
61. Wieb Bosma, Computation of cyclotomic polynomials with Magma, Computational Algebra and Number Theory (Sydney, 1992), Math. Appl., vol. 325, Kluwer Acad. Publ., Dordrecht, 1995, pp. 213–225.^[MR]
62. Wieb Bosma, Some computational experiments in number theory, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 1–30.^[MR]
63. Wieb Bosma, John Cannon, and Allan Steel, Lattices of compatibly embedded finite fields, J. Symbolic Comput. 24 (1997), no. 3-4, 351–369.^[MR]
64. Wieb Bosma, Karma Dajani, and Cor Kraaikamp, Entropy quotients and correct digits in number-theoretic expansions, Dynamics and Stochastics, IMS Lecture Notes Monogr. Ser., vol. 48, Inst. Math. Statist., Beachwood, OH, 2006, pp. 176–188.^[MR]
65. Wieb Bosma and Ben Kane, The Aliquot constant, preprint (2009), 16 pages.^[arXiv]
66. Wieb Bosma and Arjen K. Lenstra, An implementation of the elliptic curve integer factorization method, Computational Algebra and Number Theory (Sydney, 1992), Math. Appl., vol. 325, Kluwer Acad. Publ., Dordrecht, 1995, pp. 119–136.^[MR]
67. Wieb Bosma and Bart de Smit, Class number relations from a computational point of view, J. Symbolic Comput. 31 (2001), no. 1-2, 97–112.^[MR]
68. Wieb Bosma and Bart de Smit, On arithmetically equivalent number fields of small degree, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 67–79.^[MR]
69. Wieb Bosma and Peter Stevenhagen, Density computations for real quadratic units, Math. Comp. 65 (1996), no. 215, 1327–1337.^[MR]
70. Wieb Bosma and Peter Stevenhagen, On the computation of quadratic 2-class groups, J. Théor. Nombres Bordeaux 8 (1996), no. 2, 283–313.^[MR]
71. Johan Bosman, On the computation of Galois representations associated to level one modular forms, preprint (2007), 15 pages.^[arXiv]
72. Alin Bostan, Pierrick Gaudry, and Éric Schost, Linear recurrences with polynomial coefficients and computation of the Cartier-Manin operator on hyperelliptic curves, Finite Fields and Applications, Lecture Notes in Comput. Sci., vol. 2948, Springer, Berlin, 2004, pp. 40–58.^[MR]
73. Nigel Boston, Galois p-groups unramified at p—a survey, Primes and knots, Contemp. Math., vol. 416, Amer. Math. Soc., Providence, RI, 2006, pp. 31–40.^[MR]
74. Nigel Boston, Galois groups of tamely ramified p-extensions, J. Théor. Nombres Bordeaux 19 (2007), no. 1, 59–70.^[MR]
75. Nigel Boston and Rafe Jones, Arboreal Galois representations, Geom. Dedicata 124 (2007), 27–35.^[MR]
76. Nigel Boston and Charles Leedham-Green, Counterexamples to a conjecture of Lemmermeyer, Arch. Math. (Basel) 72 (1999), no. 3, 177–179.^[MR]
77. 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.
78. Irene I. Bouw and Brian Osserman, Some 4-point Hurwitz numbers in positive characteristic, preprint (2009), 23 pages.^[arXiv]
79. Carl Bracken, Eimear Byrne, Nadya Markin, and Gary McGuire, A few more quadratic APN functions, preprint (2008), 12 pages.^[arXiv]
80. Carl Bracken, Eimear Byrne, Nadya Markin, and Gary McGuire, New families of quadratic almost perfect nonlinear trinomials and multinomials, Finite Fields Appl. 14 (2008), no. 3, 703–714.^[MR]
81. Aaron Bradord, Michael Monagan, and Colin Percival, Integer factorization and computing discrete logarithms in Maple, in Proceedings of the 2006 Maple Conference, 2006, pp. 2–13.
82. A. Bremner and Jean-Joël Delorme., On equal sums of ninth powers, Math. Comp 79 (2009), 603–612.
83. A. Bremner and N. Tzanakis, Lucas sequences whose 12th or 9th term is a square, J. Number Theory 107 (2004), no. 2, 215–227.^[MR]
84. A. Bremner and N. Tzanakis, Lucas sequences whose 8th term is a square, preprint (2004), 44 pages.^[arXiv]
85. A. Bremner and N. Tzanakis, On squares in Lucas sequences, J. Number Theory 124 (2007), no. 2, 511–520.^[MR]
86. Andrew Bremner, On the equation Y²=X⁵ + k, Experiment. Math. 17 (2008), no. 3, 371–374.^[MR]
87. Andrew Bremner, A problem of Ozanam, Proc. Edinb. Math. Soc. (2) 52 (2009), no. 1, 37–44.^[MR/doi]
88. Andrew Bremner and Nikos Tzanakis, On the equation Y² = X⁶ + k, Annales des Sciences Mathématiques du Québec, to appear (2010), 23 pages.^[arXiv]
89. Richard P. Brent, Factorization of the tenth Fermat number, Math. Comp. 68 (1999), no. 225, 429–451.^[MR]
90. Richard P. Brent, Recent progress and prospects for integer factorisation algorithms, Computing and Combinatorics (Sydney, 2000), Lecture Notes in Comput. Sci., vol. 1858, Springer, Berlin, 2000, pp. 3–22.^[MR]
91. Richard P. Brent, Note on Marsaglia's xorshift random number generators, J. Stat. Soft 11 (2004), no. 5, 1-5.
92. Richard P. Brent, Peter L. Montgomery, Herman J. J. te Riele, Henk Boender, Stephania Cavallar, Conrad Curry, Bruce Dodson, Jens Franke, Joseph Leherbauer, George Sassoon, and Robert Silverman, Factorizations of cunningham numbers with bases 13 to 99: millennium edition, Report – Modelling, Analysis and Simulation, vol. 7, Centrum voor Wiskunde en Informatica, Amsterdam, 2001, pp. i-viii, pp. 1-19.
93. Richard P. Brent and Paul Zimmermann, Ten new primitive binary trinomials, Math. Comp. 78 (2009), no. 266, 1197–1199.^[MR]
94. R. de la Bret'che and T. D. Browning, Manin's conjecture for quartic del Pezzo surfaces with a conic fibration, preprint (2008).^[arXiv]
95. Florian Breuer, Ernest Lötter, and Brink van der Merwe, Ducci-sequences and cyclotomic polynomials, Finite Fields Appl. 13 (2007), no. 2, 293–304.^[MR]
96. 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]
97. Marcus Brinkmann and Gregor Leander, On the classification of APN functions up to dimension five, Des. Codes Cryptogr. 49 (2008), no. 1-3, 273–288.^[MR]
98. David Brown, The Chabauty-Coleman bound at a prime of bad reduction, preprint (2008), 10 pages.^[arXiv]
99. David Brown, Primitive integral solutions to x² + y³ = z¹⁰, preprint (2009), 11 pages.^[arXiv]
100. Ezra Brown and Bruce T. Myers, Elliptic curves from Mordell to Diophantus and back, Amer. Math. Monthly 109 (2002), no. 7, 639–649.^[MR]
101. Jim Brown, Saito-Kurokawa lifts and applications to the Bloch-Kato conjecture, Compos. Math. 143 (2007), no. 2, 290–322.^[MR]
102. N. Bruin and E. V. Flynn, n-covers of hyperelliptic curves, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 3, 397–405.^[MR]
103. N. Bruin, K. Győry, L. Hajdu, and Sz. Tengely, Arithmetic progressions consisting of unlike powers, Indag. Math. (N.S.) 17 (2006), no. 4, 539–555.^[MR]
104. Nils Bruin, Visualising Sha[2] in abelian surfaces, Math. Comp. 73 (2004), no. 247, 1459–1476 (electronic).^[MR]
105. Nils Bruin, The primitive solutions to x³+y⁹=z², J. Number Theory 111 (2005), no. 1, 179–189.^[MR]
106. Nils Bruin, Some ternary Diophantine equations of signature (n,n,2), Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 63–91.^[MR]
107. Nils Bruin, The arithmetic of Prym varieties in genus 3, Compos. Math. 144 (2008), no. 2, 317–338.^[MR/link]
108. Nils Bruin and Kevin Doerksen, The arithmetic of genus two curves with (4,4)-split Jacobians, preprint (2010), 22 pages.^[arXiv]
109. 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]
110. 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]
111. Nils Bruin and Michael Stoll, Deciding existence of rational points on curves: an experiment, Experiment. Math. 17 (2008), no. 2, 181–189.^[MR/arXiv]
112. Nils Bruin and Michael Stoll, Two-cover descent on hyperelliptic curves, preprint (2008), 19 pages.^[arXiv]
113. 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]
114. Jan Hendrik Bruinier and Tonghai Yang, CM-values of Hilbert modular functions, Invent. Math. 163 (2006), no. 2, 229-288.
115. Armand Brumer and Kenneth Kramer, Paramodular abelian varieties of odd conductor, preprint (2010).^[arXiv]
116. Ralph H. Buchholz, Triangles with three rational medians, J. Number Theory 97 (2002), no. 1, 113–131.^[MR]
117. Ralph H. Buchholz and James A. MacDougall, Cyclic polygons with rational sides and area, J. Number Theory 128 (2008), no. 1, 17–48.^[MR]
118. Yann Bugeaud, Florian Luca, Maurice Mignotte, and Samir Siksek, On Fibonacci numbers with few prime divisors, Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 2, 17–20.^[MR]
119. Yann Bugeaud, Florian Luca, Maurice Mignotte, and Samir Siksek, On perfect powers in Lucas sequences, Int. J. Number Theory 1 (2005), no. 3, 309–332.^[MR]
120. Yann Bugeaud, Maurice Mignotte, and Samir Siksek, Sur les nombres de Fibonacci de la forme q^ky^p, C. R. Math. Acad. Sci. Paris 339 (2004), no. 5, 327–330.^[MR]
121. Yann Bugeaud, Maurice Mignotte, and Samir Siksek, Classical and modular approaches to exponential Diophantine equations I: Fibonacci and Lucas perfect powers, Ann. of Math. (2) 163 (2006), no. 3, 969–1018.^[MR]
122. Yann Bugeaud, Maurice Mignotte, and Samir Siksek, Classical and modular approaches to exponential Diophantine equations II: The Lebesgue-Nagell equation, Compos. Math. 142 (2006), no. 1, 31–62.^[MR]
123. Yann Bugeaud, Maurice Mignotte, and Samir Siksek, A multi-Frey approach to some multi-parameter families of Diophantine equations, Canad. J. Math. 60 (2008), no. 3, 491–519.^[MR/link]
124. 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]
125. Jessica F. Burkhart, Neil J. Calkin, Shuhong Gao, Justine C. Hyde-Volpe, Kevin James, Hiren Maharaj, Shelly Manber, Jared Ruiz, and Ethan Smith, Finite field elements of high order arising from modular curves, Des. Codes Cryptogr. 51 (2009), no. 3, 301–314.^[MR/doi]
126. M. R. Bush, Computation of Galois groups associated to the 2-class towers of some quadratic fields, J. Number Theory 100 (2003), no. 2, 313–325.^[MR]
127. Cecilia Busuioc, The Steinberg symbol and special values of L-functions, Trans. Amer. Math. Soc. 360 (2008), no. 11, 5999–6015.^[MR]
128. Kevin Buzzard, Questions about slopes of modular forms, Astérisque (2005), no. 298, 1–15.^[MR]
129. Kevin Buzzard and Frank Calegari, A counterexample to the Gouvêa-Mazur conjecture, C. R. Math. Acad. Sci. Paris 338 (2004), no. 10, 751–753.^[MR]
130. 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]
131. Kevin Buzzard and William A. Stein, A mod five approach to modularity of icosahedral Galois representations, Pacific J. Math. 203 (2002), no. 2, 265–282.^[MR]
132. Nigel P. Byott, James E. Carter, Cornelius Greither, and Henri Johnston, On the restricted hilbert-speiser and leopoldt properties, Illinois J. Math, to appear (2011), 15 pages.^[arXiv]
133. Bryden Cais, Serre's conjectures, Preprint (2005), 21 pages.^[link]
134. Frank Calegari and Nathan M. Dunfield, Automorphic forms and rational homology 3-spheres, Geom. Topol. 10 (2006), 295–329 (electronic).^[MR/arXiv]
135. Frank Calegari and William A. Stein, Conjectures about discriminants of Hecke algebras of prime level, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 3076, Springer, Berlin, 2004, pp. 140–152.^[MR]
136. I. N. Cangül, M. Demirci, G. Soydan, and N. Tzanakis., On the diophantine equation x²+5^a·11^b=yⁿ, Funct. Approx. Comment. Math, to appear (2011), 21 pages.^[arXiv]
137. David G. Cantor and Daniel M. Gordon, Factoring polynomials over p-adic fields, Algorithmic Number Theory (Leiden, 2000), Lecture Notes in Comput. Sci., vol. 1838, Springer, Berlin, 2000, pp. 185–208.^[MR]
138. Robert Carls, Theta null points of 2-adic canonical lifts, preprint (2005), 18 pages.^[arXiv]
139. Robert Carls, Explicit Frobenius lifts on elliptic curves, preprint (2009), 26 pages.^[arXiv]
140. Robert Carls, Fast point counting on genus two curves in characteristic three, preprint (2010).^[arXiv]
141. 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]
142. Donald I. Cartwright and Tim Steger, Application of the Bruhat–Tits tree of SU₃(h) to some A₂ groups, J. Austral. Math. Soc. Ser. A 64 (1998), no. 3, 329–344.^[MR]
143. Carlos Castaño-Bernard, Further properties of a function of Ogg and Ligozat, Ramanujan J. 17 (2008), no. 1, 107–121.^[MR]
144. Wouter Castryck, Hendrik Hubrechts, and Frederik Vercauteren, Computing zeta functions in families of C_{a, b} curves using deformation, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, Springer, 2008, pp. 296-311.
145. Murat Cenk and Ferruh Özbudak, On multiplication in finite fields, J. Complexity 26 (2010), no. 2, 172–186.^[doi]
146. Antoine Chambert-Loir, Compter (rapidement) le nombre de solutions d'equations dans les corps finis, preprint (2006), 46 pages.^[arXiv]
147. Hugo Chapdelaine, Computation of p-units in ray class fields of real quadratic number fields, Math. Comp. 78 (2009), 2307–2345.
148. Robin Chapman, Steven T. Dougherty, Philippe Gaborit, and Patrick Solé, 2-modular lattices from ternary codes, J. Théor. Nombres Bordeaux 14 (2002), no. 1, 73–85.^[MR]
149. Denis Xavier Charles, Complex multiplication tests for elliptic curves, preprint (2004), 13 pages.^[arXiv]
150. Denis Charles and Kristin Lauter, Computing modular polynomials, LMS J. Comput. Math. 8 (2005), 195–204 (electronic).^[MR]
151. Imin Chen, A Diophantine equation associated to X₀(5), LMS J. Comput. Math. 8 (2005), 116–121 (electronic).^[MR]
152. Imin Chen, On the equation s² + y^2p = α³, Math. Comp. 77 (2008), no. 262, 1223–1227.^[MR]
153. Imin Chen and Chris Cummins, Elliptic curves with nonsplit mod 11 representations, Math. Comp. 73 (2004), no. 246, 869–880 (electronic).^[MR]
154. Imin Chen, Ian Kiming, and Jonas B. Rasmussen, On congruences mod p^m between eigenforms and their attached Galois representations, J. Number Theory 130 (2010), no. 3, 608–619.^[MR/doi]
155. Imin Chen and Samir Siksek, Perfect powers expressible as sums of two cubes, J. Algebra 322 (2009), no. 3, 638–656.^[MR/doi]
156. C. Chisholm and J. A. MacDougall, Rational and Heron tetrahedra, J. Number Theory 121 (2006), no. 1, 153–185.^[MR]
157. C. Chisholm and J. A. MacDougall, Rational tetrahedra with edges in geometric progression, J. Number Theory 128 (2008), no. 2, 251–262.^[MR]
158. Javier Cilleruelo, The least common multiple of a quadratic sequence, Compositio Mathematica, to appear (2010), 26 pages.^[arXiv]
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