Arithmetic properties of series of reciprocals of algebraic integers

Abstract

We obtain results bounding the degree of the series ${\sum }_{n=1}^{\infty }1/{\alpha }_n$, where $\{{\alpha }_n\}$ is a sequence of algebraic integers satisfying certain algebraic conditions and growth conditions. Our results extend results of Erdős, Hančl and Nair.

arXiv comment16 pages, an oversight has been corrected and the presentation improved