References: |
BCP97 W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), 235{265. Bos07 J. Bosman, A polynomial with Galois group SL2(F16), LMS J. Comput. Math. 10 (2007), 378{388. Bru99 S. Brueggeman, The nonexistence of certain Galois extensions unramified outside 5, J. Number Theory 75 (1999), 47{52. Bru01 S. Brueggeman, Septic number fields which are ramified only at one small prime, J. Symbolic Comput. 31 (2001), 549{555. Bru05 S. Brueggeman, The nonexistence of certain nonsolvable Galois extensions of number fields of small degree, Int. J. Number Theory 1 (2005), 155{160. BDJ08 K. Buzzard, F. Diamond and F. Jarvis, On Serre's conjecture for mod ` Galois representations over totally real fields, Preprint, arXiv:0810.2106v5, Duke Math. J., to appear. Car86 H. Carayol, Sur les representations `-adiques associees aux formes modulaires de Hilbert, Ann. Sci. Ecole Norm. Sup. (4) 19 (1986), 409{468. CQ05 G. Cardona and J. Quer, Field of moduli and field of definition for curves of genus 2, in Computational aspects of algebraic curves, Lecture Notes Series on Computing, vol. 13 (World Scientific, Hackensack, NJ, 2005), 71{83. CL07 J. Cremona and M. Lingham, Finding all elliptic curves with good reduction outside a given set of primes, Expo. Math. 16 (2007), 303{312. Dem05 L. Dembele, Explicit computations of Hilbert modular forms on Q( p 5), Expo. Math. 14 (2005), 457{466. Dem09 L. Dembele, A non-solvable Galois extension of Q ramified at 2 only, C. R. Math. Acad. Sci. Paris 347 (2009), 111{116. Dic58 L. E. Dickson, Linear groups: with an exposition of the Galois field theory (Dover, New York, 1958). Elk98a N. Elkies, Explicit modular towers, in Proceedings of the thirty-fifth annual Allerton conference on communication, control and computing, Urbana, IL, 1997, eds T. Basar and A. Vardy (University of Illinois at Urbana-Champaign, 1998), 23{32. Elk98b N. Elkies, Shimura curve computations, in Algorithmic number theory, Portland, OR, 1998, Lecture Notes in Computer Science, vol. 1423 (Springer, Berlin, 1998), 1{47. Ell05 J. Ellenberg, Serre's conjecture over F9, Ann. of Math. (2) 161 (2005), 1111{1142. Fon85 J.-M. Fontaine, Il n'y a pas de variete abelienne sur Z, Invent. Math. 81 (1985), 515{538. GL79 P. Gerardin and J. P. Labesse, The solution of a base change problem for GL(2) (following Langlands, Saito, Shintani), in Automorphic forms, representations, and L-functions, Proceedings of Symposia in Pure Mathematics, vol. 33 (American Mathematical Society, Providence, RI, 1979). GLS96 D. Gorenstein, R. Lyons and R. Solomon, The classification of the finite simple groups, Number 2, Mathematical Surveys and Monographs, vol. 40.2 (American Mathematical Society, Providence, RI, 1996). GV09 M. Greenberg and J. Voight, Computing systems of Hecke eigenvalues associated to Hilbert modular forms, Math. Comp., to appear. Gro98 B. Gross, Modular forms (mod p) and Galois representations, Int. Math. Res. Not. IMRN 16 (1998), 865{875. Gro99 B. Gross, Algebraic modular forms, Israel J. Math. 113 (1999), 61{93. HM01 F. Hajir and C. Maire, Tamely ramified towers and discriminant bounds for number fields, Compositio. Math. 128 (2001), 35{53. HM02 F. Hajir and C. Maire, Tamely ramified towers and discriminant bounds for number fields. II, J. Symbolic Comput. 33 (2002), 415{423. Hid81 H. Hida, On abelian varieties with complex multiplication as factors of the Jacobians of Shimura curves, Amer. J. Math. 103 (1981), 727{776. Jar99 F. Jarvis, Mazur's principle for totally real fields of odd degree, Compositio Math. 116 (1999), 39{79. Jon J. Jones, Tables of number fields with prescribed ramification, http://hobbes.la.asu.edu/NFDB. JR99 J. Jones and D. Roberts, Sextic number fields with discriminant (1)j2a3b, in Number theory, Ottawa, ON, 1996, CRM Proceedings & Lecture Notes, vol. 19 (American Mathematical Society, Providence, RI, 1999), 141{172. KW09 C. Khare and J.-P. Wintenberger, On Serre's conjecture for 2-dimensional mod p representations of Gal(Q=Q), Ann. of Math. (2) 169 (2009), 229{253. Kna92 A. Knapp, Elliptic curves, Mathematical Notes, vol. 40 (Princeton University Press, Princeton, NJ, 1992). LP02 J. Lansky and D. Pollack, Hecke algebras and automorphic forms, Compositio Math. 130 (2002), 21{48. Les S. Lesseni, Decic number fields ramified only at one small prime, Preprint, http://www.math.unicaen.fr/lesseni/PAGEWEB/sujet.ps, Int. J. Number Theory, submitted. Les06a S. Lesseni, The non-existence of nonsolvable octic number fields ramified only at one small prime, Math. Comp. 75 (2006), 1519{1526. Les06b S. Lesseni, Nonsolvable nonic number fields ramified only at one small prime, J. Theor. Nombres Bordeaux 18 (2006), 617{625. Mar82 J. Martinet, Petits discriminants des corps de nombres, in Journee arithmetiques 1980, Exeter, 13{19 April 1980, London Mathematical Society Lecture Note Series, vol. 56 (Cambridge University Press, Cambridge, 1982), 151{193. MW84 B. Mazur and A. Wiles, Class fields of abelian extensions of Q, Invent. Math. 76 (1984), 179{330. Moo00 H. Moon, Finiteness results on certain mod p Galois representations, J. Number Theory 84 (2000), 156{165. Odl90 A. M. Odlyzko, Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: a survey of recent results, J. Theor. Nombres Bordeaux 2 (1990), 119{141. Rob D. P. Roberts, Nonsolvable polynomials with field discriminant 5A, Preprint, http://cda.morris.umn.edu/roberts/research/five.pdf, Int. J. Number Theory, to appear. Sch03 R. Schoof, Abelian varieties over cyclotomic fields with good reduction everywhere, Math. Ann. 325 (2003), 413{448. Ser73 J.-P. Serre, Congruences et formes modulaires [d'apres H. P. F. Swinnerton-Dyer], in Seminaire Bourbaki, 24e annee (1971/1972), exp. no. 416, Lecture Notes in Mathematics, vol. 317 (Springer, Berlin, 1973), 319{338. Ser87 J.-P. Serre, Sur les representations modulaires de degre 2 de Gal(Q=Q), Duke Math. J. 54 (1987), 197{230. Ser97 J.-P. Serre, Abelian `-adic representations and elliptic curves, Research Notes in Mathematics, vol. 7 (A. K. Peters, Wellesley, MA, 1997). Ser09 J.-P. Serre, Un complement a la Note de Lassina Dembfiele. A non-solvable Galois extension of Q ramified at 2 only, C. R. Math. Acad. Sci. Paris 347 (2009), 117{118. ST97 N. I. Shepherd-Barron and R. Taylor, mod 2 and mod 5 icosahedral representations, J. Amer. Math. Soc. 10 (1997), 283{298. Shi67 G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math. (2) 85 (1967), 58{159. Shi78 G. Shimura, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), 637{679. SW01 C. M. Skinner and A. J. Wiles, Nearly ordinary deformations of irreducible residual representations, Ann. Fac. Sci. Toulouse Math. (6) 10 (2001), 185{215. Tat94 J. Tate, The non-existence of certain Galois extensions of Q unramified outside 2, Contemp. Math. 174 (1994), 153{156. Tay89 R. Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math 98 (1989), 265{280. Voi05 J. Voight, Quadratic forms and quaternion algebras: algorithms and arithmetic, PhD thesis, University of California, Berkeley, 2005. Voi09a J. Voight, Computing fundamental domains for cofinite Fuchsian groups, J. Theor. Nombres Bordeaux 21 (2009), 467{489. Voi09b J. Voight, Shimura curves of genus at most two, Math. Comp. 78 (2009), 1155{1172. Wie08 G. Wiese, On projective linear groups over finite fields as Galois groups over the rational numbers, in Modular forms on Schiermonnikoog, eds Bas Edixhoven, Gerard van der Geer and Ben Moonen (Cambridge University Press, Cambridge, 2008), 343{350. Wil88 A. Wiles, On ordinary -adic representations associated to modular forms, Invent. Math 94 (1988), 529{573. |