Identities for the Ramanujan zeta function

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