Ramanujan identities of higher degree

Abstract

We use techniques regarding generalized Dirichlet series developed in Franke (Ramanujan J 46(1):91–102, 2018) to obtain formulas for a wide class of L-functions at rational arguments. It is shown that these values are related to special functions on the upper half plane which possess similar properties as modular forms. Several formulas of Ramanujan involving values of L-functions at integer arguments turn out to be special cases of the main theorem.