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Original Articles

Numerical Verification of the Stark-Chinburg Conjecture for Some Icosahedral Representations

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Pages 419-432 | Published online: 05 Apr 2012

REFERENCES

  • Basmaji , J. 2002 . “A Table of As-Fields with Discriminant up to 40272.” [Basmaji 02], Private communication
  • Basmaji , J. and Kiming , I. 1994 . “A Table of As-Fields.” . In On Artin's Conjecture for Odd 2-Dimensional Representations 37 – 46 . Berlin : Springer-Verlag. . [Basmaji and Kiming 94], Lecture Note in Math., 1585
  • Brown , K. 1994 . Cohomology of Groups. New York : Springer-Verlag. . [Brown 94]
  • Buhler , J. 1978 . Icosahedral Galois Representations. New York : Springer-Verlag. . [Buhler 78], Lecture Notes in Math., 654
  • Burns , D. 2001 . “Equivariant Tamagawa Numbers and Galois Module Theory.” . Compositio Math. , 129 : 203 – 237 . [Burns 01]
  • Buzzard , K. , Dickinson , M. , Shepherd-Baron , N. and Taylor , R. 2001 . “On Icosahedral Artin Representations.” . Duke Math Journal , 109 ( 2 ) : 283 – 318 . [Buzzard et al. 01]
  • Chinburg , T. 1983 . “Stark's Conjecture for L-Functions with First-Order Zeroes at s = 0.” . Adv. in Math. , 48 : 82 – 113 . [Chinburg 83]
  • Cohen , H. 1993 . A Course in Computational Algebraic Number Theory. New York : Springer-Verlag. . [Cohen 93]
  • Cohen , H. 2000 . Advanced Topics in Computational Number Theory. New York : Springer-Verlag. . [Cohen 00]
  • Crespo , T. 1992 . “Extensions de An par C4 comme groupes de Galois.” . C. R. Acad. Sci. Paris , 315 : 625 – 628 . [Crespo 92]
  • Dummit , D. , Sands , J. and Tangedal , B. 1997 . “Computing Stark Units for Totally Real Cubic Fields.” . Math. Comp. , 66 : 1239 – 1267 . [Dummit et al. 97]
  • Fogel , K. 1998 . “Stark's Conjecture for Octahedral Extensions.” , PhD diss. Austin : University of Texas. . [Fogel 98]
  • Frey , G. 1994 . On Artin's Conjecture for Odd 2-Dimensional Representations New York : Springer-Verlag. . [Frey 94], Lecture Notes in Math. 1585
  • Jehanne , A. 2001 . “Realization over Q of the Groups Ã5 Â 5.” . J. Number Theory , 89 : 340 – 368 . [Jehanne 01]
  • Jehanne , A. and Müller , M. 2000 . “Modularity of an Odd Icosahedral Representation.” . J. Théorie des Nombres de Bordeaux , 12 ( 2 ) : 475 – 482 . [Jehanne and Müller 00]
  • Jehanne , A. and Müller , M. 2001 . “Modularity of Some Odd Icosahedral Representations.” [Jehanne and Müller 01], Available from World Wide Web http://www.math.u-bordeaux.fr/∼jehanne/
  • Herbrand , J. 1930 . “Nouvelle démonstration et généralisation d'un théoréme de Minkowski.” . C. R. Acad. Sci. Paris , 191 : 1282 – 1285 . [Herbrand 30]
  • Herbrand , J. 1931 . “Sur les unités d'un corps algébrique.” . C. R. Acad. Sci. Paris , 192 : 24 – 27 . [Herbrand 31]
  • Kiming , I. 1994 . “On the Experimental Verification of the Artin Conjecture for 2-Dimensional Odd Galois Representations over. Lifting of 2-Dimensional Projective Galois Representations over.” . In On Artin's Conjecture for Odd 2-Dimensional Representations 1 – 36 . Berlin : Springer-Verlag. . [Kiming 94], Lecture Notes in Math., 1585
  • Kiming , I. and Wang , X. 1994 . “Examples of 2-Dimensional Odd Galois Representations of A5-Type over Satisfying the Artin Conjecture.” . In On Artin's Conjecture for Odd 2-Dimensional Representations 109 – 121 . Berlin : Springer-Verlag. . [Kiming and Wang 94], Lecture Notes in Math., 1585
  • Minkowski , H. 1900 . “Zur Theorie der Einheiten in den algebraischen Zahlkorpern.” . Gbttinger Nachrichten , : 90 – 93 . [Minkowski 00]
  • Batut , C. , Belabas , K. , Bernardi , D. , Cohen , H. and Olivier , M. 2003 . “The Number Theory System PARI.” [PARI 03], Available from World Wide Web http://www.parigp-home.de/
  • Popescu , C. 2003 . “Base Change for Stark-Type Conjectures ‘over’.” . J. reine angew. Math. , [Popescu 03], To appear
  • Roblot , X.-F. 2000 . “Stark's Conjectures and Hilbert's Twelfth Problem.” . Experimental Math. , 9 : 251 – 260 . [Roblot 00]
  • Rubin , K. 1996 . “A Stark Conjecture ‘over Z’ for Abelian L-Functions with Multiple Zeros.” . Annales de ITnstitut Fourier , 46 : 33 – 62 . [Rubin 96]
  • Sands , J. 1987 . “Stark's Conjecture and Abelian L-Functions with Higher Order Zeros at s = 0.” . Adv. in Math. , 66 : 62 – 87 . [Sands 87]
  • Stark , H. M. 1975 . “. L-Functions at s = 1. II. Artin L-Functions with Rational Characters.” . Adv. in Math. , 17 : 60 – 92 . [Stark 75]
  • Stark , H. M. 1976 . L-Functions at s = 1. III. Totally Real Fields and Hilbert's Twelfth Problem.” . Adv. in Math. , 22 : 64 – 84 . [Stark 76]
  • Stark , H. M. 1977 . “Class Fields for Real Quadratic Fields and L-Series at 1.” . In Algebraic Number Fields Edited by: Frohlich , A. 55 – 375 . London-New York-San Francisco : Academic Press. . [Stark 77]
  • Stark , H. M. 1980 . “L-Functions at s = 1. IV. First Derivatives at s = 0.” . Adv. in Math. , 35 : 197 – 235 . [Stark 80]
  • Stark , H. M. 1981 . “Derivatives of L-series at s = 0.” . In Automorphic Forms, Representation Theory and Arithmetic (Bombay, 1979) 261 – 273 . Bombay : Tata Inst. Fund. Res. . [Stark 81], Tata Inst. Fund. Res. Studies in Math., 10
  • Tate , J. T. 1984 . Les conjectures de Stark sur les fonctions L d'Artin en s = 0. Boston : Birkhäuser. . [Tate 84]

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