31
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Stark's Conjectures and Hilbert's Twelfth Problem

Pages 251-260 | Published online: 04 Apr 2012

REFERENCES

  • Bach , E. and Sorenson , J. 1996 . “Explicit bounds for primes in residue classes” . Math. Comp. , 65 ( 216 ) : 1717 – 1735 . [Bach and Sorenson 1996]
  • Batut , C. , Belabas , K. , Bernardi , D. , Cohen , H. and Olivier , M. 1999 . “Pari-GP, version 2.0” [Batut et al. 1999], software, See ftp://megrez.math.u-bordeaux.fr/pub/pari
  • Cohen , H. and Roblot , X.-F. 2000 . “Computing the Hilbert class field of a real quadratic field” . Math. Comp. , 69 : 1229 – 1244 . [Cohen and Roblot 2000], See http://www.math.u-bordeaux.fr/~cohen/
  • Cohen , H. , Diaz y Diaz , F. and Olivier , M. 1996 . “Algorithmic techniques for relative extensions of number fields” [Cohen et al. 1996], preprint
  • Cohen , H. , Diaz y Diaz , F. and Olivier , M. 1998 . “Computing ray class groups, conductors and discriminants” . Math. Comp. , 67 ( 222 ) : 773 – 795 . [Cohen et al. 1998]
  • Daberkow , M. and Pohst , M. 1995 . “Computations with relative extensions of number fields with an application to the construction of Hilbert class fields” 68 – 76 . New York : ACM Press. . [Daberkow and Pohst 1995], Proc. ISSAC'95
  • Dummit , D. and Tangedal , B. “Computing the leading term of an abelian L-function” . Algorithmic number theory: third international symposium, ANTS-III . Portland , OR . Edited by: Buhler , J. P. pp. 400 – 411 . Berlin : Springer. . [Dummit and Tangedal 1998], Lecture Notes in Comp. Sci. 1423
  • Dummit , D. S. , Sands , J. W. and Tangedal , B. A. 1997 . “Computing Stark units for totally real cubic fields” . Math. Comp. , 66 ( 219 ) : 1239 – 1267 . [Dummit et al. 1997]
  • Fieker , C. 2000 . “Computing class fields via the Artin map” . Math. Comp. , [Fieker 2000], to appear in, PII S0025–5718(00)01255–2
  • Friedman , E. 1988 . “Hecke's integral formula” Talence : Univ. Bordeaux I. . [Friedman 1988], Exp. No. 5, 23 in Séminaire de Théorie des Nombres, 1987–1988
  • Lang , S. 1983 . Fundamentals of Diophantine geometry New York : Springer. . [Lang 1983]
  • Martinet , J. 1977 . “Character theory and Artin L-functions”. ” . In Algebraic number fields: L-functions and Galois properties (Durham, 1975) Edited by: Fröhlich , A. 1 – 87 . London : Academic Press. . [Martinet 1977]
  • Roblot , X.-F. 1997 . Algorithmes de factorisation dans les extensions relatives et applications de la conjecture de Stark à la construction des corps de classes de rayon , Thèse Talence : Université Bordeaux I. . [Roblot 1997]
  • Stark , H. M. 1971 . “Values of L-functions at s = 1, I: L-functions for quadratic forms” . Advances in Math. , 7 : 301 – 343 . [Stark 1971], (1971)
  • Stark , H. M. 1975 . “L-functions at s = 1, II: Artin L-functions with rational characters” . Advances in Math. , 17 ( 1 ) : 60 – 92 . [Stark 1975]
  • Stark , H. M. 1976 . “L-functions at s = 1, III: Totally real fields and Hilbert's twelfth problem” . Advances in Math. , 22 ( 1 ) : 64 – 84 . [Stark 1976]
  • Stark , H. M. 1980 . “L-functions at s = 1, IV: First derivatives at s = 0” . Adv. in Math. , 35 ( 3 ) : 197 – 235 . [Stark 1980]
  • Tate , J. 1984 . Les conjectures de Stark sur les fonctions L d'Artin en s = 0 Boston : Birkhäuser. . [Tate 1984]
  • Tollis , E. 1997 . “Zeros of Dedekind zeta functions in the critical strip” . Math. Comp. , 66 ( 219 ) : 1295 – 1321 . [Tollis 1997]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.