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 -