| [1] |
Laurent Bartholdi and Michael R. Bush.
Maximal unramified 3-extensions of imaginary quadratic fields and
SL2(Z3).
J. Number Theory, 124(1):159–166, 2007. |
| [2] |
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.
arXiv:0706.1466v1 [math.AG], 13 pages, 2007. |
| [3] |
M. Bauer, M. J. Jacobson, Jr., Y. Lee, and R. Scheidler.
Construction of hyperelliptic function fields of high three-rank.
Math. Comp., 77(261):503–530 (electronic), 2008. |
| [4] |
Amnon Besser and Rob De Jeu.
li(p)-service? an algorithm for computing p-adic
polyalgorithms.
Math. Comp., 77(262):1105–1134, 2008. |
| [5] |
Wieb Bosma.
Computation of cyclotomic polynomials with Magma.
In Computational Algebra and Number Theory (Sydney,
1992), volume 325 of Math. Appl., pages 213–225. Kluwer Acad. Publ.,
Dordrecht, 1995. |
| [6] |
Wieb Bosma and Bart de Smit.
On arithmetically equivalent number fields of small degree.
In Algorithmic Number Theory (Sydney, 2002), volume 2369 of
Lecture Notes in Comput. Sci., pages 67–79. Springer, Berlin, 2002. |
| [7] |
Wieb Bosma and Peter Stevenhagen.
On the computation of quadratic 2-class groups.
J. Théor. Nombres Bordeaux, 8(2):283–313, 1996. |
| [8] |
Nigel Boston.
Galois p-groups unramified at p—a survey.
In Primes and knots, volume 416 of Contemp. Math., pages
31–40. Amer. Math. Soc., Providence, RI, 2006. |
| [9] |
Nigel Boston.
Galois groups of tamely ramified p-extensions.
J. Théor. Nombres Bordeaux, 19(1):59–70, 2007. |
| [10] |
Nigel Boston and Rafe Jones.
Arboreal Galois representations.
Geom. Dedicata, 124:27–35, 2007. |
| [11] |
Nigel Boston and Charles Leedham-Green.
Counterexamples to a conjecture of Lemmermeyer.
Arch. Math. (Basel), 72(3):177–179, 1999. |
| [12] |
M. R. Bush.
Computation of Galois groups associated to the 2-class towers of
some quadratic fields.
J. Number Theory, 100(2):313–325, 2003. |
| [13] |
H. Cohen, F. Diaz y Diaz, and M. Olivier.
Subexponential algorithms for class group and unit computations.
J. Symbolic Comput., 24(3-4):433–441, 1997. |
| [14] |
Henri Cohen.
A survey of computational class field theory.
J. Théor. Nombres Bordeaux, 11(1):1–13, 1999. |
| [15] |
B. de Smit and H. W. Lenstra, Jr.
Linearly equivalent actions of solvable groups.
J. Algebra, 228(1):270–285, 2000. |
| [16] |
Bart de Smit.
On arithmetically equivalent fields with distinct p-class
numbers.
J. Algebra, 272(2):417–424, 2004. |
| [17] |
Darrin Doud.
Supersingular Galois representations and a generalization of a
conjecture of Serre.
Experiment. Math., 16, 119–128 pages, 2007. |
| [18] |
Kirsten Eisenträger and Kristin Lauter.
Computing Igusa class polynomials via the chinese remainder theory.
arXiv:math.NT/04053505 v1, 2004. |
| [19] |
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(2):723–741, 2006. |
| [20] |
Claus Fieker.
Applications of the class field theory of global fields.
In Discovering Mathematics with Magma, volume 19 of Algorithms Comput. Math., pages 31–62. Springer, Berlin, 2006. |
| [21] |
Claus Fieker.
Sparse representation for cyclotomic fields.
Experiment. Math., 16(4):493–500, 2007. |
| [22] |
Claus Fieker.
Minimizing representations over number fields ii: Computations in the
Brauer group.
J. Algebra, 322(3):752–765, 2009. |
| [23] |
Claus Fieker and Michael E. Pohst.
Dependency of units in number fields.
Math. Comp., 75(255):1507–1518 (electronic), 2006. |
| [24] |
Claus Fieker and Michael E. Pohst.
A lower regulator bound for number fields.
J. Number Theory, 128(10):2767–2775, 2008. |
| [25] |
Felix Fontein.
The infrastructure of a global field of arbitrary unit rank.
arXiv:0809.1685, 36 pages, 2008. |
| [26] |
David Ford, Sebastian Pauli, and Xavier-François Roblot.
A fast algorithm for polynomial factorization over Qp.
J. Théor. Nombres Bordeaux, 14(1):151–169, 2002. |
| [27] |
Robert Fraatz.
On the computation of integral closures of cyclic extensions of
function fields.
LMS J. Comput. Math., 10:141–160 (electronic), 2007. |
| [28] |
S. P. Glasby.
Generators for the group of units of Zn.
Austral. Math. Soc. Gaz., 22(5):226–228, 1995. |
| [29] |
Norbert Goeb.
Computing the automorphism groups of hyperelliptic function fields.
arXiv:math.NT/0305284, 16 pages, 2003. |
| [30] |
Sherry Gong.
On a problem regarding coefficients of cyclotomic polynomials.
J. Number Theory, In Press, 2009. |
| [31] |
Jordi Guardia, Jesus Montes, and Enric Nart.
Higher Newton polygons in the computation of discriminants and
prime ideal decomposition in number fields.
arXiv:0807.4065v3 [math.NT], 24 pages, 2008. |
| [32] |
Emmanuel Hallouin and Christian Maire.
Cancellation in totally definite quaternion algebras.
J. Reine Angew. Math., 595:189–213, 2006. |
| [33] |
Emmanuel Hallouin and Marc Perret.
On the kernel of the norm in some unramified number fields
extensions.
arXiv:0706.0417, 6 pages, 2007. |
| [34] |
Stephan Hell.
Die Nenner des Kontsevich-Integrals und ein spezieller
Drinfeld-Assoziator.
PhD thesis, Freie Universität Berlin, July 2002. |
| [35] |
F. Hess.
An algorithm for computing isomorphisms of algebraic function fields.
In Algorithmic Number Theory, volume 3076 of Lecture
Notes in Comput. Sci., pages 263–271. Springer, Berlin, 2004. |
| [36] |
Florian Hess, Sebastian Pauli, and Michael E. Pohst.
Computing the multiplicative group of residue class rings.
Math. Comp., 72(243):1531–1548 (electronic), 2003. |
| [37] |
David Hubbard.
Dihedral side extensions and class groups.
J. Number Theory, 128(4):731–737, 2008. |
| [38] |
Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, and Florence
Soriano-Gafiuk.
Computation of 2-groups of narrow logarithmic divisor classes of
number fields.
Journal of Symbolic Computation, To appear, 2008. |
| [39] |
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(3):715–732, 2008. |
| [40] |
Henri Johnston.
On the trace map between absolutely abelian number fields of equal
conductor.
Acta Arith., 122(1):63–74, 2006. |
| [41] |
John W. Jones and David P. Roberts.
A database of local fields.
J. Symbolic Comput., 41(1):80–97, 2006. |
| [42] |
John Jossey.
Galois 2-extensions unramified outside 2.
J. Number Theory, 124(1):42–56, 2007. |
| [43] |
Masanari Kida.
Kummer theory for norm algebraic tori.
J. Algebra, 293(2):427–447, 2005. |
| [44] |
Masanari Kida, Yuichi Rikuna, and Atsushi Sato.
Classifying Brumer's quintic polynomials by weak Mordell-Weil
groups.
arXiv:math.NT/0802.0054v1, 10 pages, 2008. |
| [45] |
Jürgen Klüners and Gunter Malle.
Counting nilpotent Galois extensions.
J. Reine Angew. Math., 572:1–26, 2004. |
| [46] |
Jürgen Klüners and Sebastian Pauli.
Computing residue class rings and Picard groups of orders.
J. Algebra, 292(1):47–64, 2005. |
| [47] |
M. Künzer and H. Weber.
Some additive Galois cohomology rings.
Comm. Algebra, 33(12):4415–4455, 2005. |
| [48] |
Matthias Künzer and Eduard Wirsing.
On coefficient valuations of Eisenstein polynomials.
J. Théor. Nombres Bordeaux, 17(3):801–823, 2005. |
| [49] |
Thorsten Lagemann.
Codes und Automorphismen optimaler Artin-Schreier-Turme.
PhD thesis, Ruprecht-Karls-Universität Heidelberg, April 2006. |
| [50] |
Y. Lee, R. Scheidler, and C. Yarrish.
Computation of the fundamental units and the regulator of a cyclic
cubic function field.
Experiment. Math., 12(2):211–225, 2003. |
| [51] |
Franck Leprévost, Michael Pohst, and Andreas Schöpp.
Units in some parametric families of quartic fields.
Acta Arith., 127(3):205–216, 2007. |
| [52] |
Aaron Levin.
Ideal class groups and torsion in Picard groups of varieties.
arXiv:0805.1361v1 [math.NT], 31 pages, 2008. |
| [53] |
Melissa L. Macasieb.
Derived arithmetic Fuchsian groups of genus two.
Experiment. Math., 17(3):347–369, 2008. |
| [54] |
Kazuo Matsuno.
Construction of elliptic curves with large Iwasawa
λ-invariants and large Tate-Shafarevich groups.
Manuscripta Math., 122(3):289–304, 2007. |
| [55] |
William G. McCallum and Romyar T. Sharifi.
A cup product in the Galois cohomology of number fields.
Duke Math. J., 120(2):269–310, 2003. |
| [56] |
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(1):231 – 245, 2009. |
| [57] |
Sebastian Pauli.
Efficient Enumeration of Extensions of Local Fields with Bounded
Discriminant.
PhD thesis, Concordia University, June 2001. |
| [58] |
Sebastian Pauli.
Constructing class fields over local fields.
J. Théor. Nombres Bordeaux, 18(3):627–652, 2006. |
| [59] |
Sebastian Pauli and Florence Soriano-Gafiuk.
The discrete logarithm in logarithmic l-class groups and its
applications in K-theory.
In Algorithmic Number Theory, volume 3076 of Lecture
Notes in Comput. Sci., pages 367–378. Springer, Berlin, 2004. |
| [60] |
René Schoof.
Arakelov class groups and ideal lattices.
Mathematisches Forschungsinstitut Oberwolfach Report No.
1/2005, pages 23–24, 2005. |
| [61] |
René Schoof.
Computing Arakelov class groups.
In Algorithmic number theory: lattices, number fields, curves
and cryptography, volume 44 of Math. Sci. Res. Inst. Publ., pages
447–495. Cambridge Univ. Press, Cambridge, 2008. |
| [62] |
Andreas M. Schöpp.
Fundamental units in a parametric family of not totally real quintic
number fields.
J. Théor. Nombres Bordeaux, 18(3):693–706, 2006. |
| [63] |
Romyar T. Sharifi.
Iwasawa theory and the Eisenstein ideal.
Duke Math. J., 137(1):63–101, 2007. |
| [64] |
Romyar T. Sharifi.
On Galois groups of unramified pro-p extensions.
Math. Ann., 342(2):297–308, 2008. |
| [65] |
William Stein and Yan Zhang.
On power bases in number fields.
Preprint, 15 pages, 2005. |
| [66] |
Aliza Steurer.
On the Galois groups of the 2-class towers of some imaginary
quadratic fields.
J. Number Theory, 125(1):235–246, 2007. |
| [67] |
Mark van Hoeij and John Cremona.
Solving conics over function fields.
J. Théor. Nombres Bordeaux, 18(3):595–606, 2006. |
| [68] |
John Voight.
The gauss higher relative class number problem.
Ann. Sci. Math. Québec, Accepted, 10 pages, 2009. |
| [69] |
Gabor Wiese.
On projective linear groups over finite fields as Galois groups
over the rational numbers.
In Edixhoven, Bas et al., Modular forms on Schiermonnikoog.
Based on the conference on modular forms, Schiermonnikoog, Netherlands,
October 2006, pages 343–350. Cambridge University Press, Cambridge, 2008. |
| [70] |
Qingquan Wu and Renate Scheidler.
An explicit treatment of biquadratic function fields.
Contrib. Discrete Math., 2(1):43–60 (electronic), 2007. |
