Larry Rolen

Affiliation: Emory University

Email: lrolen@emory.edu

Title Of Talk: Integrality Properties of the CM-Values of Certain Weak Maass Forms

Abstract: In a recent paper, Bruinier and Ono prove that the coefficients of certain weight $-1/2$ harmonic Maass forms are traces of singular moduli for weak Maass forms. In particular, for the partition function $p(n)$, they prove that \[ p(n) =\frac{1}{24n-1}\cdot\sum P(\alpha_Q), \] where $P$ is a weak Maass form and $Q$ ranges over a finite set of discriminant $-24n + 1$ CM points. Moreover, they show that $6\cdot(24n-1)\cdot P(\alpha_Q)$ is always an algebraic integer, and they conjecture that $(24n-1)\cdot P(\alpha_Q)$ is always an algebraic integer. Here we prove a general theorem which implies this conjecture as a corollary.

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