Submit progress

on Irrationality of the Riemann zeta value at 5

The statement

The Riemann zeta function is defined for a complex number $s$ with real part greater than $1$ by

\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}.

A real number is said to be irrational if it cannot be expressed as a ratio of two integers. Prove that $\zeta(5)$ is irrational. Equivalently, prove that there exists an irrational number $x$ such that $\zeta(5) = x$ .

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.