An extension of Rohrlich's Theorem to the $j$-function

Abstract

In this paper, we extend Rohrlich's Theorem on the integral of logarithms of meromorphic functions to compute the inner product between such functions and polynomials in the $j$-function. We then show that the generating function for these inner products with $j_n$ is part of a weight two modular object.

References in corpus (2)

• Polyharmonic Maass forms for PSL(2, Z)
• On two arithmetic theta lifts