Identities for the Ramanujan zeta function

Abstract

We prove formulas for special values of the Ramanujan tau zeta function. Our formulas show that $L(\Delta ,k)$ is a period in the sense of Kontsevich and Zagier when $k\ge 12$. As an illustration, we reduce $L(\Delta ,k)$ to explicit integrals of hypergeometric and algebraic functions when $k\in \{12,13,14,15\}$.

10 pages