The irrationality of some number theoretical series

TL;DR

This paper proves the irrationality of certain factorial series by combining elementary, analytic number theory, and uniform distribution methods, advancing understanding of the properties of number theoretical series.

Contribution

It introduces a novel approach by integrating elementary and analytic techniques with uniform distribution theory to establish irrationality results for factorial series.

Findings

Proved the irrationality of specific factorial series.

Developed a new method combining multiple mathematical disciplines.

Enhanced understanding of the properties of number theoretical series.

Abstract

We prove the irrationality of some factorial series. To do so we combine methods from elementary and analytic number theory with methods from the theory of uniform distribution.