%0 Journal Article
%T Gaps and the exponent of convergence of an integer sequence
%A Georges Grekos
%A Martin Sleziak
%A Jana Tomanov¨˘
%J Uniform Distribution Theory
%D 2011
%I Mathematical Institute of the Slovak Academy of Sciences
%X Professor Tibor  al¨˘t, at one of his seminars at Comenius University, Bratislava, asked to study the influence of gaps of an integer sequence $A={a_1 < a_2 < \dots < a_n < \dots}$ 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  al¨˘t's question and we study the influence of the sequence of ratios $({\frac{a_m}{a_{m+1}}})_{m=1}^\infty}$ and of the sequence $({\frac{a_{m+1}-a_m}{a_{m}}})_{m=1}^\infty}$ on the upper and on the lower exponential densities of $A$.
%K Integer sequence
%K densities
%K exponent of convergence
%U http://www.boku.ac.at/MATH/udt/vol06/no2/09GreSlTo11-2.pdf