Hypergeometric rational approximations to $\zeta (4)$

Abstract

We give a new hypergeometric construction of rational approximations to $\zeta (4)$, which absorbs the earlier one from 2003 based on Bailey's ${}_9{F}_8$ hypergeometric integrals. With the novel ingredients we are able to get a better control of arithmetic and produce a record irrationality measure for $\zeta (4)$.

24 pages