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On Divisors of Modular Forms by Bringmann, Kathrin; Kane, Ben; Löbrich, Steffen; Ono, Ken; Rolen, Larry is a scholarly article available to read on EtoBox.

What is On Divisors of Modular Forms about?

The denominator formula for the Monster Lie algebra is the product expansion for the modular function $j(z)-j(\tau)$ given in terms of the Hecke system of $\operatorname{SL}_2(\mathbb Z)$-modular functions $j_n(\tau)$. It is prominent in Zagier's seminal paper on traces of singular moduli, and in the Duncan-Frenkel work on Moonshine. The formula is equivalent to the description of the generating function for the $j_n(z)$ as a weight 2 modular form with a pole at $z$. Although these results rely on the fact that $X_0(1)$ has genus 0, here we obtain a generalization, framed in terms of polar harmonic Maass forms, for all of the $X_0(N)$ modular curves. We use these functions to study divisors of modular forms.

Author

Bringmann, Kathrin; Kane, Ben; Löbrich, Steffen; Ono, Ken; Rolen, Larry

Published

2016

Language

EN