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Group Topologies on the Integers and S-Unit Equations. / Skresanov, S. V.
в: Siberian Mathematical Journal, Том 61, № 3, 01.05.2020, стр. 542-544.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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