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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 303, Pages 258–278
DOI: https://doi.org/10.1134/S0371968518040192 (Mi tm3943) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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
Full-text PDF (277 kB) Citations (5)
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DOI: https://doi.org/10.1134/S0371968518040192
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.
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.
Received: April 7, 2018
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 303, Pages 239–258
DOI: https://doi.org/10.1134/S0081543818080199
Bibliographic databases:
Document Type: Article
UDC: 511.32
MSC: 11B30, 11L40, 11T30
Language: Russian
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, Trudy 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 Trudy Mat. Inst. Steklova
\yr 2018
\vol 303
\pages 258--278
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
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  • https://doi.org/10.1134/S0371968518040192
  • https://www.mathnet.ru/eng/tm/v303/p258
    • This publication is cited in the following 5 articles:
    1. Bryce Kerr, Ali Mohammadi, Igor E. Shparlinski, “Additive Energy of Polynomial Images”, SIAM J. Discrete Math., 38:3 (2024), 2163  crossref
    2. Sam Mansfield, Akshat Mudgal, “A quadratic Vinogradov mean value theorem in finite fields”, The Quarterly Journal of Mathematics, 75:3 (2024), 1007  crossref
    3. Ali Mohammadi, Alina Ostafe, Igor E. Shparlinski, “On some matrix counting problems”, Journal of London Math Soc, 110:6 (2024)  crossref
    4. Hanson B., Petridis G., “Refined Estimates Concerning Sumsets Contained in the Roots of Unity”, Proc. London Math. Soc., 122:3 (2021), 353–358  crossref  mathscinet  isi
    5. W. Banks, I. Shparlinski, “Congruences with intervals and arbitrary sets”, Arch. Math., 114:5 (2020), 527–539  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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