Abelian fields and the Brumer-Stark conjecture

J. W. Sands

Compositio Mathematica (1984)

  • Volume: 53, Issue: 3, page 337-346
  • ISSN: 0010-437X

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Sands, J. W.. "Abelian fields and the Brumer-Stark conjecture." Compositio Mathematica 53.3 (1984): 337-346. <http://eudml.org/doc/89692>.

@article{Sands1984,
author = {Sands, J. W.},
journal = {Compositio Mathematica},
keywords = {Jacobi-sum Hecke characters; abelian extension; Artin L-function; Brumer-Stark conjecture; Stickelberger element; cyclotomic field; Gauss sums; integrality results},
language = {eng},
number = {3},
pages = {337-346},
publisher = {Martinus Nijhoff Publishers},
title = {Abelian fields and the Brumer-Stark conjecture},
url = {http://eudml.org/doc/89692},
volume = {53},
year = {1984},
}

TY - JOUR
AU - Sands, J. W.
TI - Abelian fields and the Brumer-Stark conjecture
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 53
IS - 3
SP - 337
EP - 346
LA - eng
KW - Jacobi-sum Hecke characters; abelian extension; Artin L-function; Brumer-Stark conjecture; Stickelberger element; cyclotomic field; Gauss sums; integrality results
UR - http://eudml.org/doc/89692
ER -

References

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  1. [1] P. Deligne and K. Ribet, Values of abelian L-functions at negative integers over totally real fields. Inventiones Mathematicae59 (1980) 227-286. Zbl0434.12009MR579702
  2. [2] B.H. Gross, P-adic L-series at s = 0, manuscript for J. Fac. Sci., U. Tokyo, Sect. IA 28 (1981), No. 3, 979-994. Zbl0507.12010MR656068
  3. [3] A. Hurwitz, Einige Eigenschaften Dirichlet'schen Funktionen. Zeit. fur Math. Phys.27 (1882) 86-101(Math WerkeI, 72-88). JFM14.0371.01
  4. [4] D. Kubert and S. Lichtenbaum, Jacobi-sum Hecke characters and Gauss sum identities. Comp Math.48 (1983) Fasc. 1, 55-87. Zbl0513.12010MR700580
  5. [5] S. Lang, Cyclotomic Fields. Springer-Verlag, New York (1978). Zbl0395.12005MR485768
  6. [6] D. Rideout, A generalization of Stickelbergers' Theorem. Ph.D. Thesis, McGill, Montreal (1970). 
  7. [7] J.W. Sands, The Conjecture of Gross and Stark for Special Values of Abelian L-series over Totally Real Fields. Ph.D. Thesis, U.C.S.D., San Diego (1982). 
  8. [8] H.M. Stark, L-functions at s =1. IV. First derivatives at s = 0, Advances in Math.35 (1980) 197-235. Zbl0475.12018MR563924
  9. [9] H.M. Stark, Values of Zeta and L-functions, to appear in proceedings of conference to honor Dedekind's 150th birthday. MR693166
  10. [10] J. Tate, Brumer-Stark-Stickelberger, Seminaire de Theorie des Nombres Annee 1980-81, expose no. 24. Zbl0504.12005MR644657
  11. [11] J. Tate, On Stark's conjectures on the behavior of L(s,X) at s = 0. J. Fac. Sci. U. Tokyo Sect. IA 28 (1981), No. 3, 963-978. Zbl0514.12013MR656067
  12. [12] A. Weil, Jacobi sums as Grössencharaktere. Trans Am. Math. Soc.23 (1952) 487-495. Zbl0048.27001MR51263
  13. [13] A. Weil, Sommes de Jacobi et caracteres de Hecke. Nachr. Akad. Wiss. Göttingen, Math.-Phys. Klasse (1974) 1-14. Zbl0367.10035MR392859

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