An algebraic characterization of the Kronecker function

Abstract

We characterize the generating series of extended period polynomials of normalized Hecke eigenforms for ${\mathrm{PSL}}_2(\mathbb{Z})$ studied by Zagier in terms of the period relations and existence of a suitable factorization. For this we prove a characterization of the Kronecker function as the `fundamental solution' to the Fay identity.

11 pages, final version, minor differences in abstract and acknowledgements compared to published version