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BOUNDS FOR TRIPLE EXPONENTIAL SUMS WITH MIXED EXPONENTIAL AND LINEAR TERMS

Part of: Diophantine equations Exponential sums and character sums

Published online by Cambridge University Press:  03 May 2018

KAM HUNG YAU
KAM HUNG YAU*
Affiliation:
Department of Pure Mathematics, University of New South Wales, Sydney, NSW 2052, Australia email kamhung.yau@unsw.edu.au
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Abstract

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We establish bounds for triple exponential sums with mixed exponential and linear terms. The method we use is by Shparlinski [‘Bilinear forms with Kloosterman and Gauss sums’, Preprint, 2016, arXiv:1608.06160] together with a bound for the additive energy from Roche-Newton et al. [‘New sum-product type estimates over finite fields’, Adv. Math.293 (2016), 589–605].

Keywords

exponential sumsexponential functioncancellationsolutions to congruences in small boxes

MSC classification

Primary: 11L07: Estimates on exponential sums
Secondary: 11D79: Congruences in many variables
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 64 - 69
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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