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Proceedings of the American Mathematical Society
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
MathSciNet review: 928961
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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?)

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  • [D-H] H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewessin zyklischen Fällen, Crelles J. 172 (1935), 151.
  • [H] David R. Hayes, Stickelberger elements in function fields, Compositio Math. 55 (1985), no. 2, 209–239. MR 795715 (87d:11091)
  • [T] John Tate, Les conjectures de Stark sur les fonctions 𝐿 d’Artin en 𝑠=0, Progress in Mathematics, vol. 47, Birkhäuser Boston, Inc., Boston, MA, 1984 (French). Lecture notes edited by Dominique Bernardi and Norbert Schappacher. MR 782485 (86e:11112)
  • [W] A. Weil, Courbes algébriques et variétés abéliennes, Hermann, Paris, 1971.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0928961-7
PII: S 0002-9939(1988)0928961-7
Article copyright: © Copyright 1988 American Mathematical Society