Stickelberger elements in function fields

David R. Hayes

Compositio Mathematica (1985)

  • Volume: 55, Issue: 2, page 209-239
  • ISSN: 0010-437X

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Hayes, David R.. "Stickelberger elements in function fields." Compositio Mathematica 55.2 (1985): 209-239. <http://eudml.org/doc/89716>.

@article{Hayes1985,
author = {Hayes, David R.},
journal = {Compositio Mathematica},
keywords = {elliptic modules; cyclotomic function fields; Iwasawa theory; p-adic group ring; partial zeta-functions; ideal class groups; Stickelberger element; Stark's Abelian conjectures; Drinfeld modules; units},
language = {eng},
number = {2},
pages = {209-239},
publisher = {Martinus Nijhoff Publishers},
title = {Stickelberger elements in function fields},
url = {http://eudml.org/doc/89716},
volume = {55},
year = {1985},
}

TY - JOUR
AU - Hayes, David R.
TI - Stickelberger elements in function fields
JO - Compositio Mathematica
PY - 1985
PB - Martinus Nijhoff Publishers
VL - 55
IS - 2
SP - 209
EP - 239
LA - eng
KW - elliptic modules; cyclotomic function fields; Iwasawa theory; p-adic group ring; partial zeta-functions; ideal class groups; Stickelberger element; Stark's Abelian conjectures; Drinfeld modules; units
UR - http://eudml.org/doc/89716
ER -

References

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  1. [1] J. Coates: B-adic L-functions and Iwasawa's theory. A. Frölich (ed.), Algebraic Number Fields. London: Academic Press (1977) 269-353. Zbl0393.12027MR460282
  2. [2] V.G. Drinfeld: Elliptic Modules (Russian). Math. Sbornik94 (1974) 594-627 = Math. USSR Sbornik23 (1974) 561-592. Zbl0321.14014MR384707
  3. [3] S. Galovich and M. Rosen: The class number of cyclotomic function fields: J. Number Theory13 (1981) 363-375. Zbl0473.12014MR634206
  4. [4] S. Galovich and M. Rosen: Units and class groups in cyclotomic functions fields. J. Number Theory14 (1982) 156-184. Zbl0483.12003MR655724
  5. [5] S. Galovich and M. Rosen: Distributions on Rational Function Fields. Math. Annalen256 (1981) 549-60. Zbl0472.12013MR628234
  6. [6] D. Goss: The Γ-ideal and special zeta values, Duke Journal (1980) 345-364. Zbl0441.12002
  7. [7] D. Goss: On a new type of L-function for algebraic curves over finite fields. Pacific Journal105 (1983) 143-181. Zbl0571.14010MR688411
  8. [8] B. Gross: The annihilation of divisor classes in abelian extensions of the rational function field. Séminaire de Théorie des Nombres(Bordeaux1980-81), exposé no. 3. Zbl0507.14020
  9. [9] D. Hayes: Explicit class field theory for rational function fields. Trans. Amer. Math. Soc.189 (1974) 77-91. Zbl0292.12018MR330106
  10. [10] D. Hayes: Explicit class field theory in global function fields. G.C. Rota (ed.), Studies in Algebra and Number Theory. New York: Academic Press (1979) 173-217. Zbl0476.12010MR535766
  11. [11] D. Hayes: Analytic class number formulas in global function fields, Inventiones Math.65 (1981) 49-69. Zbl0491.12014MR636879
  12. [12] D. Hayes: Elliptic units in function fields, in Proc. of a Conference on Modern Developments Related to Fermat's Last Theorem, D. Goldfeld ed., Birkhauser, Boston (1982). Zbl0499.12012MR685307
  13. [13] H. Stark: L-functions at s = 1. IV. First derivatives at s = 0. Advances in Math.35 (1980) 197-235. Zbl0475.12018MR563924
  14. [14] J. Tate: Les conjectures de Stark sur les functions L d'Artin en s = 0, Birkhauser, Boston (1984). Zbl0545.12009MR782485
  15. [15] J. Tate: Brumer-Stark-Stickelberger, Séminaire de Théorie des Numbres, Université de Bordeaux (1980-81), exposé no. 24. Zbl0504.12005MR644657
  16. [16] J. Tate: On Stark's conjectures on the behavior of L(s, χ) at s = 0. Jour. Fac. Science, Univ. of Tokyo, 28 (1982), 963-978. Zbl0514.12013

Citations in EuDML Documents

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  1. Fei Xu, Jianqiang Zhao, Maximal independent systems of units in global function fields
  2. Hassan Oukhaba, Sign functions of imaginary quadratic fields and applications
  3. Ernst-Ulrich Gekeler, Méthodes analytiques rigides dans la théorie arithmétique des corps de fonctions
  4. Harald Niederreiter, Chaoping Xing, Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places
  5. Harald Niederreiter, Chaoping Xing, Drinfeld modules of rank 1 and algebraic curves with many rational points. II

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