Note On the Irrationality of the L-Function Constants L(s, X)

TL;DR

This paper presents a unified proof demonstrating the irrationality of special values of the beta L-function, including the Catalan constant, for integers greater than one, suggesting these constants are irrational.

Contribution

It provides the first unified proof of irrationality for L(n, X) values, including the Catalan constant, advancing understanding of their arithmetic nature.

Findings

Proof confirms irrationality of L(n, X) for n > 1

First evidence suggesting Catalan constant is irrational

Unified approach applicable to multiple L-function values

Abstract

A unified proof of the irrationality of the special values L(n, X), n > 1 an integer, of the beta L-function is put forward in this note. The first case of n = 2 seems to confirm that the Catalan constant L(2, X) is an irrational number.