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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 314, Pages 145–151
DOI: https://doi.org/10.4213/tm4190 (Mi tm4190) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups

Máté Matolcsiab, Imre Z. Ruzsab

a Budapest University of Technology and Economics (BME), Egry J. u. 1, H-1111 Budapest, Hungary
b Alfréd Rényi Institute of Mathematics, P.O. Box 127, H-1364 Budapest, Hungary
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DOI: https://doi.org/10.4213/tm4190
Abstract: By constructing suitable nonnegative exponential sums, we give upper bounds on the cardinality of any set $B_q$ in cyclic groups $\mathbb Z_q$ such that the difference set $B_q-B_q$ avoids cubic residues modulo $q$.
Funding agency Grant number
Hungarian National Research, Development and Innovation Office K132097
K129335
M. Matolcsi was supported by the NKFIH grant nos. K132097 and K129335. I. Z. Ruzsa was supported by the NKFIH grant no. K129335.
Received: August 1, 2020
Revised: November 29, 2020
Accepted: June 17, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 314, Pages 138–143
DOI: https://doi.org/10.1134/S0081543821040088
Bibliographic databases:
Document Type: Article
UDC: 511.172
Language: Russian
Citation: Máté Matolcsi, Imre Z. Ruzsa, “Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups”, Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 314, Steklov Math. Inst., Moscow, 2021, 145–151; Proc. Steklov Inst. Math., 314 (2021), 138–143
Citation in format AMSBIB
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\paper Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups
\inbook Analytic and Combinatorial Number Theory
\bookinfo Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 314
\pages 145--151
\publ Steklov Math. Inst.
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4190}
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\jour Proc. Steklov Inst. Math.
\yr 2021
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\pages 138--143
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    • This publication is cited in the following 1 articles:
    1. E. Naslund, “Paley graphs and Sárközy's theorem in function fields”, The Quarterly Journal of Mathematics, 74:2 (2023), 627  crossref  mathscinet  zmath
    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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