Article
Gaps and the Exponent of Convergence of an Integer Sequence
Authors
, and
Abstract
Professor Tibor Šalát, at one of his seminars at Comenius University,
Bratislava, asked to study the influence of gaps of an integer sequence
\(A = \{a_1 < a_2 < \cdots < a_n < \ldots\}\) 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
\(\left(\dfrac{a_m}{a_{m+1}}\right)_{m=1}^{\infty}\) and of the sequence
\(\left(\dfrac{a_{m+1} - a_m}{a_m}\right)_{m=1}^{\infty}\) on the upper and
on the lower exponential densities of \(A\).
Keywords
Integer sequence, densities, exponent of convergence.
Citation
Grekos, G., Sleziak, M., & Tomanova, J. (2011). Gaps and the exponent of convergence of an integer sequence. Uniform Distribution Theory, 6(2), 117–130.
G. Grekos, M. Sleziak and J. Tomanova, “Gaps and the exponent of convergence of an integer sequence,” Uniform Distribution Theory, vol. 6, no. 2, pp. 117–130, 2011.
Grekos G, Sleziak M, Tomanova J. Gaps and the exponent of convergence of an integer sequence. Uniform Distribution Theory. 2011;6(2):117–130.
Grekos, G., Sleziak, M. and Tomanova, J. (2011), ‘Gaps and the exponent of convergence of an integer sequence’, Uniform Distribution Theory, 6(2), pp. 117–130.
Grekos, Georges, et al. “Gaps and the Exponent of Convergence of an Integer Sequence.” Uniform Distribution Theory, vol. 6, no. 2, 2011, pp. 117–130.
Grekos, Georges, Martin Sleziak, and Jana Tomanova. “Gaps and the Exponent of Convergence of an Integer Sequence.” Uniform Distribution Theory 6, no. 2 (2011): 117–130.
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Published by: Engineering Journals
