Bounds of Gauss sums in finite fields

Author:
Igor E. Shparlinski

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2817-2824

MSC (2000):
Primary 11L05, 11T24; Secondary 11B37

DOI:
https://doi.org/10.1090/S0002-9939-04-07133-3

Published electronically:
June 2, 2004

MathSciNet review:
2063098

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider Gauss sums of the form

with a nontrivial additive character of a finite field of elements of characteristic . The classical bound becomes trivial for . We show that, combining some recent bounds of Heath-Brown and Konyagin with several bounds due to Deligne, Katz, and Li, one can obtain the bound on which is nontrivial for the values of of order up to . We also show that for almost all primes one can obtain a bound which is nontrivial for the values of of order up to .

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Additional Information

**Igor E. Shparlinski**

Affiliation:
Department of Computing, Macquarie University, Sydney, New South Wales 2109, Australia

Email:
igor@ics.mq.edu.au

DOI:
https://doi.org/10.1090/S0002-9939-04-07133-3

Keywords:
Gauss sums,
finite fields,
linear recurrence sequences

Received by editor(s):
February 1, 2002

Received by editor(s) in revised form:
June 7, 2002

Published electronically:
June 2, 2004

Communicated by:
Wen-Ching Winnie Li

Article copyright:
© Copyright 2004
American Mathematical Society