S. V. Skresanov, “Group topologies on the integers and <nobr>$s$</nobr>-unit equations”, Sibirsk. Mat. Zh., 2020, Volume 61, Number 3,Pages <nobr>687

This article is cited in 1 paper

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

S. V. Skresanov^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

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.

UDC: 512.546.2+511.52

MSC: 35R30

Received: 05.02.2020
Revised: 05.02.2020
Accepted: 19.02.2020

DOI: 10.33048/smzh.2020.61.317