Number Theory

Algebraic Number Theory

11Rxx and 11Sxx

  1. Avner Ash, Jos Brakenhoff, and Theodore Zarrabi, Equality of polynomial and field discriminants, Experiment. Math. 16 (2007), no. 3, 367–374.[MR/link]
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  6. Wieb Bosma, Canonical bases for cyclotomic fields, Appl. Algebra Engrg. Comm. Comput. 1 (1990), no. 2, 125–134.[MR]
  7. 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]
  8. 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]
  9. Wieb Bosma and Peter Stevenhagen, On the computation of quadratic 2-class groups, J. Théor. Nombres Bordeaux 8 (1996), no. 2, 283–313.[MR]
  10. 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]
  11. Nigel Boston, Galois groups of tamely ramified p-extensions, J. Théor. Nombres Bordeaux 19 (2007), no. 1, 59–70.[MR]
  12. Nigel Boston and Rafe Jones, Arboreal Galois representations, Geom. Dedicata 124 (2007), 27–35.[MR]
  13. Nigel Boston and Charles Leedham-Green, Counterexamples to a conjecture of Lemmermeyer, Arch. Math. (Basel) 72 (1999), no. 3, 177–179.[MR]
  14. 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]
  15. 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]
  16. Murat Cenk and Ferruh Özbudak, On multiplication in finite fields, J. Complexity 26 (2010), no. 2, 172–186.[doi]
  17. H. Cohen, F. Diaz y Diaz, and M. Olivier, Subexponential algorithms for class group and unit computations, J. Symbolic Comput. 24 (1997), no. 3-4, 433–441.[MR]
  18. Henri Cohen, A survey of computational class field theory, J. Théor. Nombres Bordeaux 11 (1999), no. 1, 1–13.[MR]
  19. Daniel Delbourgo and Thomas Ward, The growth of CM periods over false Tate extensions, Experiment. Math. 19 (2010), no. 2, 195–210.[MR/link]
  20. 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]
  21. Lassina Dembele, Matthew Greenberg, and John Voight, Nonsolvable number fields ramified only at 3 and 5, preprint (2009), 18 pages.[arXiv]
  22. Darrin Doud, Supersingular Galois representations and a generalization of a conjecture of Serre, Experiment. Math. 16 (2007), no. 1, 119–128.[MR/link]
  23. Kirsten Eisenträger and Kristin Lauter, Computing Igusa class polynomials via the chinese remainder theory, preprint (2004).[arXiv]
  24. Jordan S. Ellenberg and Akshay Venkatesh, The number of extensions of a number field with fixed degree and bounded discriminant, Ann. of Math. (2) 163 (2006), no. 2, 723–741.[MR]
  25. Claus Fieker, Applications of the class field theory of global fields, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 31–62.[MR]
  26. Claus Fieker, Sparse representation for cyclotomic fields, Experiment. Math. 16 (2007), no. 4, 493–500.[MR]
  27. Claus Fieker, Minimizing representations over number fields II. Computations in the Brauer group, J. Algebra 322 (2009), no. 3, 752–765.[MR/doi]
  28. Claus Fieker and Michael E. Pohst, Dependency of units in number fields, Math. Comp. 75 (2006), no. 255, 1507–1518 (electronic).[MR]
  29. Claus Fieker and Michael E. Pohst, A lower regulator bound for number fields, J. Number Theory 128 (2008), no. 10, 2767–2775.[MR]
  30. Felix Fontein, The infrastructure of a global field of arbitrary unit rank, preprint (2008), 36 pages.[arXiv]
  31. David Ford, Sebastian Pauli, and Xavier-François Roblot, A fast algorithm for polynomial factorization over Qp, J. Théor. Nombres Bordeaux 14 (2002), no. 1, 151–169.[MR]
  32. Robert Fraatz, On the computation of integral closures of cyclic extensions of function fields, LMS J. Comput. Math. 10 (2007), 141–160 (electronic).[MR]
  33. 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]
  34. S. P. Glasby, Generators for the group of units of Zn, Austral. Math. Soc. Gaz. 22 (1995), no. 5, 226–228.[MR]
  35. Norbert Goeb, Computing the automorphism groups of hyperelliptic function fields, preprint (2003), 16 pages.[arXiv]
  36. Ralph Greenberg, On the structure of certain Galois cohomology groups, Doc. Math. (2006), no. Extra Vol., 335–391 (electronic).[MR]
  37. J. Guardia, J. Montes, and E. Nart, Higher Newton polygons and integral bases, preprint (2009).[arXiv]
  38. Jordi Guardia, Jesus Montes, and Enric Nart, Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields, preprint (2008), 24 pages.[arXiv]
  39. Lajos Hajdu, Optimal systems of fundamental S-units for LLL-reduction, Period. Math. Hungar. 59 (2009), no. 1, 53–79.[MR/doi]
  40. Emmanuel Hallouin and Christian Maire, Cancellation in totally definite quaternion algebras, J. Reine Angew. Math. 595 (2006), 189–213.[MR]
  41. Emmanuel Hallouin and Marc Perret, On the kernel of the norm in some unramified number fields extensions, preprint (2007), 6 pages.[arXiv]
  42. Stephan Hell, Die nenner des kontsevich-integrals und ein spezieller drinfeld-assoziator, PhD Thesis, Freie Universität Berlin, 2002.
  43. F. Hess, An algorithm for computing isomorphisms of algebraic function fields, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 3076, Springer, Berlin, 2004, pp. 263–271.[MR]
  44. Florian Hess, Sebastian Pauli, and Michael E. Pohst, Computing the multiplicative group of residue class rings, Math. Comp. 72 (2003), no. 243, 1531–1548 (electronic).[MR]
  45. Mark van Hoeij and John Cremona, Solving conics over function fields, J. Théor. Nombres Bordeaux 18 (2006), no. 3, 595–606.[MR]
  46. David Hubbard, Dihedral side extensions and class groups, J. Number Theory 128 (2008), no. 4, 731–737.[MR]
  47. Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, and Florence Soriano-Gafiuk, Computation of 2-groups of positive classes of exceptional number fields, J. Théor. Nombres Bordeaux 20 (2008), no. 3, 715–732.[MR]
  48. Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, and Florence Soriano-Gafiuk, Computation of 2-groups of narrow logarithmic divisor classes of number fields, J. Symbolic Comput. 44 (2009), no. 7, 852–863.[MR/doi]
  49. Henri Johnston, On the trace map between absolutely abelian number fields of equal conductor, Acta Arith. 122 (2006), no. 1, 63–74.[MR]
  50. John W. Jones and David P. Roberts, A database of local fields, J. Symbolic Comput. 41 (2006), no. 1, 80–97.[MR]
  51. John Jossey, Galois 2-extensions unramified outside 2, J. Number Theory 124 (2007), no. 1, 42–56.[MR]
  52. Masanari Kida, Kummer theory for norm algebraic tori, J. Algebra 293 (2005), no. 2, 427–447.[MR]
  53. Masanari Kida, A Kummer theoretic construction of an S3-polynomial with given quadratic subfield, Interdisciplinary Information Sciences 16 (2010), no. 1, 17–20.[doi]
  54. Masanari Kida, Descent Kummer theory via Weil restriction of multiplicative groups, J. of Number Theory 130 (2010), no. 3, 639–659.[doi]
  55. Masanari Kida, Guénaël Renault, and Kazuhiro Yokoyama, Quintic polynomials of Hashimoto-Tsunogai, Brumer and Kummer, Int. J. Number Theory 5 (2009), no. 4, 555–571.[MR/doi]
  56. Masanari Kida, Yuichi Rikuna, and Atsushi Sato, Classifying Brumer's quintic polynomials by weak Mordell-Weil groups, IJNT 6 (2010), no. 3, 691–704.[doi]
  57. Norbert Klingen, Leopoldt's conjecture for imaginary Galois number fields, J. Symbolic Comput. 10 (1990), no. 6, 531–545.[MR]
  58. Jürgen Klüners and Gunter Malle, Counting nilpotent Galois extensions, J. Reine Angew. Math. 572 (2004), 1–26.[MR]
  59. Jürgen Klüners and Sebastian Pauli, Computing residue class rings and Picard groups of orders, J. Algebra 292 (2005), no. 1, 47–64.[MR]
  60. Elisavet Konstantinou and Aristides Kontogeorgis, Computing polynomials of the Ramanujan tn class invariants, Canad. Math. Bull. 52 (2009), no. 4, 583–597.[MR/link]
  61. M. Künzer and H. Weber, Some additive Galois cohomology rings, Comm. Algebra 33 (2005), no. 12, 4415–4455.[MR]
  62. Matthias Künzer and Eduard Wirsing, On coefficient valuations of Eisenstein polynomials, J. Théor. Nombres Bordeaux 17 (2005), no. 3, 801–823.[MR]
  63. Thorsten Lagemann, Codes und automorphismen optimaler artin-schreier-turme, PhD Thesis, Ruprecht-Karls-Universität Heidelberg, 2006.
  64. Y. Lee, R. Scheidler, and C. Yarrish, Computation of the fundamental units and the regulator of a cyclic cubic function field, Experiment. Math. 12 (2003), no. 2, 211–225.[MR]
  65. Franck Leprévost, Michael Pohst, and Andreas Schöpp, Units in some parametric families of quartic fields, Acta Arith. 127 (2007), no. 3, 205–216.[MR]
  66. Aaron Levin, Ideal class groups and torsion in Picard groups of varieties, preprint (2008), 31 pages.[arXiv]
  67. Melissa L. Macasieb, Derived arithmetic Fuchsian groups of genus two, Experiment. Math. 17 (2008), no. 3, 347–369.[MR/arXiv]
  68. Piotr Maciak, Primes of the form x2+n*y2 in function fields, preprint (2009), 12 pages.[arXiv]
  69. 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]
  70. William G. McCallum and Romyar T. Sharifi, A cup product in the Galois cohomology of number fields, Duke Math. J. 120 (2003), no. 2, 269–310.[MR]
  71. Harris Nover, Computation of Galois groups associated to the 2-class towers of some imaginary quadratic fields with 2-class group C2×C2×C2, Journal of Number Theory 129 (2009), no. 1, 231–245.[doi]
  72. Sebastian Pauli, Efficient enumeration of extensions of local fields with bounded discriminant, PhD Thesis, Concordia University, 2001.
  73. Sebastian Pauli, Constructing class fields over local fields, J. Théor. Nombres Bordeaux 18 (2006), no. 3, 627–652.[MR]
  74. Sebastian Pauli and Florence Soriano-Gafiuk, The discrete logarithm in logarithmic l-class groups and its applications in K-theory, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 3076, Springer, Berlin, 2004, pp. 367–378.[MR]
  75. Diana Savin, About certain prime numbers, preprint (2009), 9.[arXiv]
  76. René Schoof, Arakelov class groups and ideal lattices, Mathematisches Forschungsinstitut Oberwolfach Report No. 1/2005 (2005), 23–24.
  77. René Schoof, Computing Arakelov class groups, Algorithmic number theory: lattices, number fields, curves and cryptography, Math. Sci. Res. Inst. Publ., vol. 44, Cambridge Univ. Press, Cambridge, 2008, pp. 447–495.[MR/arXiv]
  78. Andreas M. Schöpp, Fundamental units in a parametric family of not totally real quintic number fields, J. Théor. Nombres Bordeaux 18 (2006), no. 3, 693–706.[MR]
  79. Romyar T. Sharifi, Iwasawa theory and the Eisenstein ideal, Duke Math. J. 137 (2007), no. 1, 63–101.[MR]
  80. Romyar T. Sharifi, On Galois groups of unramified pro-p extensions, Math. Ann. 342 (2008), no. 2, 297–308.[MR]
  81. B. de Smit and H. W. Lenstra, Jr., Linearly equivalent actions of solvable groups, J. Algebra 228 (2000), no. 1, 270–285.[MR]
  82. Bart de Smit, On arithmetically equivalent fields with distinct p-class numbers, J. Algebra 272 (2004), no. 2, 417–424.[MR]
  83. Bart de Smit and Robert Perlis, Zeta functions do not determine class numbers, Bull. Amer. Math. Soc. (N.S.) 31 (1994), no. 2, 213–215.[MR]
  84. William Stein and Yan Zhang, On power bases in number fields, Preprint (2005), 15 pages.
  85. Aliza Steurer, On the Galois groups of the 2-class towers of some imaginary quadratic fields, J. Number Theory 125 (2007), no. 1, 235–246.[MR]
  86. Stéphane Vinatier, Structure galoisienne dans les extensions faiblement ramifiées de Q, J. Number Theory 91 (2001), no. 1, 126–152.[MR/doi]
  87. John Voight, The gauss higher relative class number problem, Ann. Sci. Math. Québec Accepted (2009), 10 pages.[arXiv]
  88. Gabor Wiese, On projective linear groups over finite fields as Galois groups over the rational numbers, Edixhoven, Bas et al., Modular forms on Schiermonnikoog. Based on the conference on modular forms, Schiermonnikoog, Netherlands, October 2006, Cambridge University Press, Cambridge, 2008, pp. 343–350.[arXiv]
  89. Qingquan Wu and Renate Scheidler, An explicit treatment of biquadratic function fields, Contrib. Discrete Math. 2 (2007), no. 1, 43–60 (electronic).[MR]
  90. Dan Yasaki, Binary Hermitian forms over a cyclotomic field, J. Algebra 322 (2009), no. 11, 4132–4142.[MR/doi]
  91. Alexey Zaytsev and Gary McGuire, On the zeta functions of an optimal tower of function fields over F4, preprint (2009), 14 pages.[arXiv]