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Trudy Mat. Inst. Steklova, 2017, Volume 296, Pages 252–259 (Mi tm3770)  

This article is cited in 5 scientific papers (total in 5 papers)

On the product sets of rational numbers

Yu. N. Shteinikov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A new lower bound on the size of product sets of rational numbers is obtained. An upper estimate for the multiplicative energy of two sets of rational numbers is also found.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968517010198

Full text: PDF file (178 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 296, 243–250

Bibliographic databases:

UDC: 511.178
Received: June 15, 2016

Citation: Yu. N. Shteinikov, “On the product sets of rational numbers”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 252–259; Proc. Steklov Inst. Math., 296 (2017), 243–250

Citation in format AMSBIB
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\vol 296
\pages 252--259
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://doi.org/10.1134/S0371968517010198
  • http://mi.mathnet.ru/eng/tm/v296/p252

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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. Yu. N. Shteinikov, “Addendum to J. Cilleruelo, D.S. Ramana, and O. Ramaré's paper “Quotient and product sets of thin subsets of the positive integers””, Proc. Steklov Inst. Math., 296 (2017), 251–255  mathnet  crossref  crossref  mathscinet  isi  elib
    2. S. V. Konyagin, M. A. Korolev, “Irreducible solutions of an equation involving reciprocals”, Sb. Math., 208:12 (2017), 1818–1834  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. S. V. Konyagin, I. D. Shkredov, “On subgraphs of random Cayley sum graphs”, European J. Combin., 70 (2018), 61–74  crossref  mathscinet  zmath  isi  scopus
    4. Yu. N. Shteinikov, “On the size of the quotient of two subsets of positive integers”, Proc. Steklov Inst. Math., 303 (2018), 259–267  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Yu. N. Shteinikov, “O razmere mnozhestva proizvedeniya mnozhestv ratsionalnykh chisel”, Chebyshevskii sb., 21:1 (2020), 357–363  mathnet  crossref
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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