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MULTIPLE EXPONENTIAL AND CHARACTER SUMS WITH MONOMIALS

Part of: Exponential sums and character sums

Published online by Cambridge University Press:  27 May 2014

Igor E. Shparlinski
Igor E. Shparlinski*
Affiliation:
Department of Pure Mathematics, University of New South Wales, Sydney, NSW 2052, Australia email igor.shparlinski@unsw.edu.au
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Abstract

We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with multiplicative characters to which previously known methods do not apply. In particular, in the case of multiplicative characters modulo a prime $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p$ we break the barrier of $p^{1/4}$ for ranges of individual variables.

MSC classification

Secondary: 11L07: Estimates on exponential sums 11L40: Estimates on character sums
Type
Research Article
Information
Mathematika , Volume 60 , Issue 2 , July 2014 , pp. 363 - 373
Copyright
Copyright © University College London 2014 

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