Abelian fields and the Brumer-Stark conjecture

J. W. Sands

Compositio Mathematica (1984)

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

How to cite


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

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},

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 -


  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.