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Group Topologies on the Integers and S-Unit Equations. / Skresanov, S. V.

In: Siberian Mathematical Journal, Vol. 61, No. 3, 01.05.2020, p. 542-544.

Research output: Contribution to journal › Article › peer-review

Harvard

Skresanov, SV 2020, 'Group Topologies on the Integers and S-Unit Equations', Siberian Mathematical Journal, vol. 61, no. 3, pp. 542-544. https://doi.org/10.1134/S0037446620030179

APA

Skresanov, S. V. (2020). Group Topologies on the Integers and S-Unit Equations. Siberian Mathematical Journal, 61(3), 542-544. https://doi.org/10.1134/S0037446620030179

Vancouver

Skresanov SV. Group Topologies on the Integers and S-Unit Equations. Siberian Mathematical Journal. 2020 May 1;61(3):542-544. doi: 10.1134/S0037446620030179

Author

Skresanov, S. V. / Group Topologies on the Integers and S-Unit Equations. In: Siberian Mathematical Journal. 2020 ; Vol. 61, No. 3. pp. 542-544.

BibTeX

@article{5f45888496a249fe9e19f5335c8c852d,
title = "Group Topologies on the Integers and S-Unit Equations",
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 = "Diophantine equation, S-unit, T-sequence, topological group",
author = "Skresanov, {S. V.}",
year = "2020",
month = may,
day = "1",
doi = "10.1134/S0037446620030179",
language = "English",
volume = "61",
pages = "542--544",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "3",

}

RIS

TY - JOUR

T1 - Group Topologies on the Integers and S-Unit Equations

AU - Skresanov, S. V.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - 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.

AB - 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.

KW - Diophantine equation

KW - S-unit

KW - T-sequence

KW - topological group

UR - http://www.scopus.com/inward/record.url?scp=85086342703&partnerID=8YFLogxK

U2 - 10.1134/S0037446620030179

DO - 10.1134/S0037446620030179

M3 - Article

AN - SCOPUS:85086342703

VL - 61

SP - 542

EP - 544

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

ID: 24519750