A note on odd zeta values

TL;DR

This paper introduces a novel approach combining rational linear forms and the saddle point method to establish the existence of at least two irrational numbers among certain odd zeta values.

Contribution

It presents a new construction of rational linear forms in odd zeta values and applies the saddle point method to prove irrationality results.

Findings

At least two irrational numbers among 33 specified odd zeta values.

New construction of rational linear forms in odd zeta values.

Application of saddle point method to number theory problems.

Abstract

Using a new construction of rational linear forms in odd zeta values and the saddle point method, we prove the existence of at least two irrational numbers amongst the 33 odd zeta values $\zeta$(5), $\zeta$(7),. .. , $\zeta$(69).