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ON SOME MULTIPLE CHARACTER SUMS

Part of: Sequences and sets Exponential sums and character sums Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  03 April 2017

Ilya D. Shkredov  and
Igor E. Shparlinski
Ilya D. Shkredov
Affiliation:
Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow 119991, Russia Institute for Information Transmission Problems of Russian Academy of Sciences, Bolshoy Karetny Per. 19, Moscow 127994, Russia email ilya.shkredov@gmail.com
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 improve a recent result of B. Hanson [Estimates for character sums with various convolutions. Preprint, 2015, arXiv:1509.04354] on multiplicative character sums with expressions of the type $a+b+cd$ and variables $a,b,c,d$ from four distinct sets of a finite field. We also consider similar sums with $a+b(c+d)$. Our new bounds rely on some recent advances in additive combinatorics.

MSC classification

Primary: 11B30: Arithmetic combinatorics; higher degree uniformity 11L07: Estimates on exponential sums 11T23: Exponential sums
Type
Research Article
Information
Mathematika , Volume 63 , Issue 2 , 2017 , pp. 553 - 560
Copyright
Copyright © University College London 2017 

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