I. D. Shkredov, I. E. Shparlinski, “Double character sums with intervals and arbitrary sets”, Trudy Mat. Inst. Steklova, 2018, Volume 303,Pages <nobr>258–278</nobr>

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Trudy Mat. Inst. Steklova, 2018 Volume 303, Pages 258–278 (Mi tm3943)

This article is cited in 5 papers

Double character sums with intervals and arbitrary sets

I. D. Shkredov^abc, I. E. Shparlinski^d

^a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
^b Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia
^c Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
^d Department of Pure Mathematics, University of New South Wales, Sydney, NSW 2052, Australia

Abstract: We obtain a new bound on certain double sums of multiplicative characters which improves several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical object of study in additive combinatorics.

Keywords: finite field, character sums, collinear triples, multiplicative energy.

UDC: 511.32

MSC: 11B30, 11L40, 11T30

Received: April 7, 2018

DOI: 10.1134/S0371968518040192

English version: Proceedings of the Steklov Institute of Mathematics, 2018, 303, 239–258

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