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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 3, Pages 687–691
DOI: https://doi.org/10.33048/smzh.2020.61.317 (Mi smj6012) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Group topologies on the integers and $s$-unit equations

S. V. Skresanovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (374 kB) Citations (1)
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DOI: https://doi.org/10.33048/smzh.2020.61.317
Abstract: A sequence of integers is called a T-sequence if there exists a Hausdorff group topology on the integers such that the sequence converges to 0. Given a finite set $S$ of primes, we construct some Hausdorff group topology on the integers such that every increasing sequence with terms divisible only by primes from $S$ converges to 0. Also we answer in the affirmative the question on T-sequences which was posed by Protasov and Zelenuk. Our results rely on a nontrivial number-theoretic fact about $S$-unit equations.
Keywords: topological group, T-sequence, $S$-unit, Diophantine equation.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences 0314-2019-0001
The work was supported by the Program of Fundamental Scientific Research of the Russian Federation (Project 0314-2019-0001).
Received: 05.02.2020
Revised: 05.02.2020
Accepted: 19.02.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 3, Pages 542–544
DOI: https://doi.org/10.1134/S0037446620030179
Bibliographic databases:
Document Type: Article
UDC: 512.546.2+511.52
MSC: 35R30
Language: Russian
Citation: S. V. Skresanov, “Group topologies on the integers and $s$-unit equations”, Sibirsk. Mat. Zh., 61:3 (2020), 687–691; Siberian Math. J., 61:3 (2020), 542–544
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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