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Mixed exponential sums over finite fields
Author(s):
Francis
N.
Castro;
Carlos
J.
Moreno
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2529-2537.
MSC (1991):
Primary 11L40;
Secondary 11S15
Posted:
February 28, 2000
MathSciNet review:
1690978
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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 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:
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- 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.
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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:
10.1090/S0002-9939-00-05441-1
PII:
S 0002-9939(00)05441-1
Received by editor(s):
October 7, 1998
Posted:
February 28, 2000
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2000,
American Mathematical Society
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