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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?)

  • [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] David R. Hayes, Stickelberger elements in function fields, Compositio Math. 55 (1985), no. 2, 209–239. MR 795715
  • [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
  • [W] A. Weil, Courbes algébriques et variétés abéliennes, Hermann, Paris, 1971.

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Article copyright: © Copyright 1988 American Mathematical Society