Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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

Abstract:

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. Enrico Bombieri, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71–105. MR 0200267 (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. Carlos Moreno, Algebraic curves over finite fields, Cambridge Tracts in Mathematics, vol. 97, Cambridge University Press, Cambridge, 1991. MR 1101140 (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. G. I. Perel′muter, Estimate of a sum along an algebraic curve, Mat. Zametki 5 (1969), 373–380 (Russian). MR 0241424 (39 #2764)
  • 7. Serre, J. P., Local Fields, Herman, Paris, 1968.
  • 8. Henning Stichtenoth, Algebraic function fields and codes, Universitext, Springer-Verlag, Berlin, 1993. MR 1251961 (94k:14016)
  • 9. André Weil, On some exponential sums, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 204–207. MR 0027006 (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
Email: fcastro@goliath.cnnet.clu.edu

Carlos J. Moreno
Affiliation: Department of Mathematics, Baruch College, CUNY, P.O. Box 545, N. Salem, New York 10560
Email: carlos@kepler.baruch.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05441-1
PII: S 0002-9939(00)05441-1
Received by editor(s): October 7, 1998
Published electronically: February 28, 2000
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society