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ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE

Published online by Cambridge University Press:  29 March 2010

VALÉRIE GILLOT  and
PHILIPPE LANGEVIN
VALÉRIE GILLOT
Affiliation:
Institut de Mathématiques de Toulon, Université du Sud Toulon-Var, France e-mail: gillot@univ-tln.fr, langevin@univ-tln.fr
PHILIPPE LANGEVIN
Affiliation:
Institut de Mathématiques de Toulon, Université du Sud Toulon-Var, France e-mail: gillot@univ-tln.fr, langevin@univ-tln.fr
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Abstract

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In this paper, we improve results of Gillot, Kumar and Moreno to estimate some exponential sums by means of q-degrees. The method consists in applying suitable elementary transformations to see an exponential sum over a finite field as an exponential sum over a product of subfields in order to apply Deligne bound. In particular, we obtain new results on the spectral amplitude of some monomials.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 315 - 324
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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