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

Double character sums with intervals and arbitrary sets

I. D. Shkredovabc, I. E. Shparlinskid

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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433
Australian Research Council DP170100786
DP180100201
The work of the first author (Section 2) is supported by the Russian Science Foundation under grant 14-11-00433. The work of the second author is supported by the Australian Research Council, grant nos. DP170100786 and DP180100201.


DOI: https://doi.org/10.1134/S0371968518040192

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

Bibliographic databases:

UDC: 511.32
MSC: 11B30, 11L40, 11T30
Received: April 7, 2018

Citation: I. D. Shkredov, I. E. Shparlinski, “Double character sums with intervals and arbitrary sets”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Tr. Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 258–278; Proc. Steklov Inst. Math., 303 (2018), 239–258

Citation in format AMSBIB
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\paper Double character sums with intervals and arbitrary sets
\inbook Harmonic analysis, approximation theory, and number theory
\bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 303
\pages 258--278
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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