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)



Mixed exponential sums over finite fields

Authors: Francis N. Castro and Carlos J. Moreno
Journal: Proc. Amer. Math. Soc. 128 (2000), 2529-2537
MSC (1991): Primary 11L40; Secondary 11S15
Published electronically: February 28, 2000
MathSciNet review: 1690978
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


In this paper we calculate the conductor of a character that consists of the product of an additive and a multiplicative character. This computation improves the bound for exponential sums given by G. I. Perel$^\prime$muter. This calculation gives an easy method to compute the conductor associated to a character of the Galois group of the composite of an Artin-Schreier extension and a Kummer extension.

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

  • 1. Bombieri, E., On exponential sums in finite fields Am. J. Math., 88(1966), 71-105. MR 34:166
  • 2. Deligne, P., Applications de la formule des traces aux sommes trigonometriques, SGA 4.5, Lectures Notes In Math., 569,(1977), 168-232.
  • 3. Deligne, P., La conjecture de Weil II, Publ. Math. I.H.E.S. 52(1981), 313-428.
  • 4. Moreno, C. J., Algebraic Curves over Finite Fields, Cambridge Tracts in Mathematics, 97, Cambridge Univ, Press, Cambridge, 1991.MR 92d:11066
  • 5. Katz, N., Gauss sums, and Monodromy groups, Ann. of Math. Stud., Princeton, 116, 9 88. N., Exponential sums and differential equations, Ann. of Math. Studies, Princeton, 124, 1990.
  • 6. Perel'muter, G. I., Estimation of a sum along an algebraic curve, Mat. Zametki, 5(1969), 373-380.MR 39:2764
  • 7. Serre, J. P., Local Fields, Herman, Paris, 1968.
  • 8. Stichtenoth, H., Algebraic Fields and Codes, Universitext Springer-Verlag, New York, 1991.MR 94k:14016
  • 9. Weil, A., On some exponential sums, Proc. Nat. Acad. Sci. U.S.A., 34(1948), 204-207. MR 10:234e

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11L40, 11S15

Retrieve articles in all journals with MSC (1991): 11L40, 11S15

Additional Information

Francis N. Castro
Affiliation: Department of Mathematics, University of Puerto Rico, Rio Piedras, College Park 274 Salerno, San Juan, Puerto Rico 00931

Carlos J. Moreno
Affiliation: Department of Mathematics, Baruch College, CUNY, P.O. Box 545, N. Salem, New York 10560

Received by editor(s): October 7, 1998
Published electronically: February 28, 2000
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society