# Hypergeometric rational approximations to $\zeta(4)$

## TL;DR

This paper introduces a new hypergeometric approach to approximate ζ(4), improving the control over arithmetic properties and establishing a record irrationality measure for this value.

## Contribution

It presents a novel hypergeometric construction that enhances previous methods and achieves a better irrationality measure for ζ(4).

## Key findings

- New hypergeometric construction for ζ(4)
- Improved irrationality measure for ζ(4)
- Enhanced control of arithmetic properties

## Abstract

We give a new hypergeometric construction of rational approximations to $\zeta(4)$, which absorbs the earlier one from 2003 based on Bailey's ${}_9F_8$ hypergeometric integrals. With the novel ingredients we are able to get a better control of arithmetic and produce a record irrationality measure for $\zeta(4)$.