A common structure of $n_k$'s for which $n_k/alpha/bmod1/to x$

Authors: Štefan Porubský, O. Strauch
Publication year: 2015
Publication type: Článek v odborném periodiku
Periodical: Publicationes Mathematicae-Debrecen
Projects: Distribution and metric properties of number sequences and their applications
Bibliographic citation: PORUBSKÝ, Štefan, STRAUCH, O. A common structure of $n_k$'s for which $n_k/alpha/bmod1/to x$. Publicationes Mathematicae-Debrecen. 2015, 86(3-4), 493-502. ISSN 0033-3883. E-ISSN 2064-2849.
ID: 445154

Abstract

In this paper the authors show, among other, that for every irrational number alpha and every real number x from the unit interval and a given decreasing sequence of positive numbers converging to 0 it is possible to construct a sequence of positive integers subject to a growing condition depending on the given decreasing sequence, which when multiplied by the given irrational number alpha converge to the given real number x.