Arithmetic properties of series of reciprocals of algebraic integers

TL;DR

This paper investigates the algebraic and growth properties of series composed of reciprocals of algebraic integers, providing bounds on their degrees and extending previous mathematical results.

Contribution

It introduces new bounds on the degrees of such reciprocal series, generalizing earlier work by Erdős, Hanczl, and Nair.

Findings

Bounds on the degree of reciprocal series of algebraic integers

Extension of previous results to broader algebraic conditions

Enhanced understanding of the algebraic structure of reciprocal series

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 Erd\H{o}s, Han\v{c}l and Nair.