Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the Frobenius endomorphisms of Fermat and Artin-Schreier curves


Author: Robert F. Coleman
Journal: Proc. Amer. Math. Soc. 102 (1988), 463-466
MSC: Primary 11G20; Secondary 14G15
DOI: https://doi.org/10.1090/S0002-9939-1988-0928961-7
MathSciNet review: 928961
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The following article offers an explanation of the relationship of Jacobi and Gauss sums to Fermat and Artin-Schreier curves which is an analogue of the proof of Stickleberger's theorem.


References [Enhancements On Off] (What's this?)

  • [G] K. F. Gauss, Disquisitiones arithmeticae, Werke, Vol. I, 1901.
  • [D-H] H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewessin zyklischen Fällen, Crelles J. 172 (1935), 151.
  • [H] D. Hayes, Stickelberger elements in function fields, Compositio Math. 55 (1985), 209-239. MR 795715 (87d:11091)
  • [T] J. Tate, Les conjectures de Stark sur les fonctions $ L$ d'Artin en $ s = 0$, Birkhäuser, Boston, Mass., 1984. MR 782485 (86e:11112)
  • [W] A. Weil, Courbes algébriques et variétés abéliennes, Hermann, Paris, 1971.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11G20, 14G15

Retrieve articles in all journals with MSC: 11G20, 14G15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0928961-7
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society