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

Kathrin Bringmann; Ben Kane

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arXiv · 1903.06868

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

Kathrin Bringmann·Ben Kane

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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.

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Kathrin Bringmann, Ben Kane. 2019-03-16. An extension of Rohrlich's Theorem to the $j$-function. https://arxiv.org/abs/1903.06868

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