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Mat. Sb., 2018, Volume 209, Number 11, Pages 60–68 (Mi msb8992)  

This article is cited in 1 scientific paper (total in 1 paper)

Sets in $\mathbb{Z}_m$ whose difference sets avoid squares

M. R. Gabdullinab

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: We prove that the bound $|A|\leq m^{1/2}(3n)^{1.5n}$ holds for all square-free $m\in\mathbb{N}$ and any set $A\subset\mathbb{Z}_m$ such that $A-A$ contains no nonzero squares, where $n$ denotes the number of odd prime divisors of $m$.
Bibliography: 9 titles.

Keywords: This research was funded by a grant of the Russian Science Foundation (project no. 14-11-00702).

Funding Agency Grant Number
Russian Science Foundation 14-11-00702


DOI: https://doi.org/10.4213/sm8992

Full text: PDF file (541 kB)
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English version:
Sbornik: Mathematics, 2018, 209:11, 1603–1610

Bibliographic databases:

UDC: 511.33
MSC: Primary 11B50; Secondary 11L03
Received: 17.07.2017 and 25.09.2017

Citation: M. R. Gabdullin, “Sets in $\mathbb{Z}_m$ whose difference sets avoid squares”, Mat. Sb., 209:11 (2018), 60–68; Sb. Math., 209:11 (2018), 1603–1610

Citation in format AMSBIB
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\by M.~R.~Gabdullin
\paper Sets in $\mathbb{Z}_m$ whose difference sets avoid squares
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\yr 2018
\vol 209
\issue 11
\pages 60--68
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\crossref{https://doi.org/10.4213/sm8992}
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\transl
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\vol 209
\issue 11
\pages 1603--1610
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  • https://doi.org/10.4213/sm8992
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Máté Matolcsi, Imre Z. Ruzsa, “Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups”, Proc. Steklov Inst. Math., 314 (2021), 138–143  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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