English

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

Number Theory 2019-09-12 v2

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 jj-function. We then show that the generating function for these inner products with jnj_n is part of a weight two modular object.

Keywords

Cite

@article{arxiv.1903.06868,
  title  = {An extension of Rohrlich's Theorem to the $j$-function},
  author = {Kathrin Bringmann and Ben Kane},
  journal= {arXiv preprint arXiv:1903.06868},
  year   = {2019}
}