Gaps and the exponent of convergence of an integer sequence
Number Theory
2012-01-11 v1
Abstract
Professor Tibor \v{S}al\'at, at one of his seminars at Comenius University, Bratislava, asked to study the influence of gaps of an integer sequence A={a_1<a_2<...<a_n<...} on its exponent of convergence. The exponent of convergence of A coincides with its upper exponential density. In this paper we consider an extension of Professor \v{S}al\'at's question and we study the influence of the sequence of ratios a_m/a_{m+1} and of the sequence (a_{m+1}-a_m)/a_m on the upper and on the lower exponential densities of A.
Cite
@article{arxiv.1201.2158,
title = {Gaps and the exponent of convergence of an integer sequence},
author = {Georges Grekos and Jana Tomanová and Martin Sleziak},
journal= {arXiv preprint arXiv:1201.2158},
year = {2012}
}