Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-30T20:46:30.612Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimates of hybrid exponential sums on quasiprojective varieties over finite fields

Part of: Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  26 February 2010

C. J. Mozzochi
C. J. Mozzochi
Affiliation:
Institute for Advanced Study, Princeton, N.J. 08540, U.S.A.
Get access

Abstract

Recently Bombieri and Sperber have jointly created a new construction for estimating exponential sums on quasiprojective varieties over finite fields. In this paper we apply their construction to estimate hybrid exponential sums on quasiprojective varieties over finite fields. In doing this we utilize a result of Aldolphson and Sperber concerning the degree of the L-function associated with a certain exponential sum.

MSC classification

Secondary: 11T23: Exponential sums
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 63 - 72
Copyright
Copyright © University College London 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Adolphson, A. and Sperber, S.. On the degree of the L-function associated with an exponential sum. Compositio Math., 68 (1988), 125–159.Google Scholar
2.Bombieri, E.. On exponential sums in finite fields. Amer. J. Math., 88 (1966), 71–105.Google Scholar
3.Bombieri, E.. On exponential sums in finite fields, II. Inventiones Math., 41 (1978), 29–39.Google Scholar
4.Bombieri, E. and Sperber, S.. On the degree of Artin L-functions in characteristic p. C.R. Acad. Sci. Paris, 306, Série I (1988), 393–398.Google Scholar
5.Bombieri, E. and Sperber, S.. On the estimation of certain exponential sums. Ada Arithmetica, 69 (1995), 329–358.Google Scholar
6.Deligne, P.. La conjecture de Weil I. Publ. Math. IHES, 43 (1974), 273–307.Google Scholar
7.Deligne, P.. La conjecture de Weil II. Publ. Math. IHES, 52 (1980), 137–252.Google Scholar
8.Dwork, B.. On the zeta function of a hypersurface III. Ann. of Math., 83 (1966), 457–519.Google Scholar
9.Iwaniec, H.. Small eigenvalues of Laplacian for ┌0(N), Acta Arith. 56 (1990), 65–82.CrossRefGoogle Scholar
10.Katz, N.. Sommes Exponentielles. Soc. Math. France, Asterisque, 79 (1980).Google Scholar
11.Lang, S.. Abelian Varieties (Springer-Verlag, New York Inc, 1983).CrossRefGoogle Scholar
12.Lidl, R. and Niederreiter, H.. Finite Fields (Cambridge University Press, New York, 1987).Google Scholar
13.Moreno, C. J.. Algebraic Curves over Finite Fields (Cambridge University Press, New York, 1991).Google Scholar
14.Serre, J.-P.. Endomorphisms complétement continus des espaces de Banach p-adiques. Publ. Math. IHES, 12 (1962).Google Scholar
15.Serre, J.-P.. Majorations de Sommes Exponentilles. Soc. Math. France, Astérisque, 41–42 (1977), 111–126.Google Scholar