Dirichlet series of integers with missing digits

Abstract

For certain sequences $A$ of positive integers with missing $g$-adic digits, the Dirichlet series $F_A(s)={\sum }_{a\in A}{a}^{-s}$ has abscissa of convergence ${\sigma }_c<1$. The number ${\sigma }_c$ is computed. This generalizes and strengthens a classical theorem of Kempner on the convergence of the sum of the reciprocals of a sequence of integers with missing decimal digits.

Minor improvements and corrected typos; 7 pages

Cited by in corpus (2)

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