Gaps and the exponent of convergence of an integer sequence

Georges Grekos; Jana Tomanová; Martin Sleziak

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arXiv · 1201.2158

Gaps and the exponent of convergence of an integer sequence

Georges Grekos·Jana Tomanová·Martin Sleziak

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Abstract

Professor Tibor Šalát, 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 Šalát'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.

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Georges Grekos, Jana Tomanová, Martin Sleziak. 2012-01-10. Gaps and the exponent of convergence of an integer sequence. https://arxiv.org/abs/1201.2158

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