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arXiv · 1107.4114

Integrality Properties of the CM-values of Certain Weak Maass Forms

Eric Larson·Larry Rolen
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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 \[p(n)=\frac{1}{24n-1} \sum P(α_Q),\] where $P$ is a weak Maass form and $α_Q$ ranges over a finite set of discriminant $-24n+1$ CM points. Moreover, they show that $6 (24n-1) P(α_Q)$ is always an algebraic integer, and they conjecture that $(24n-1) P(α_Q)$ is always an algebraic integer. Here we prove a general theorem which implies this conjecture as a corollary.

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Eric Larson, Larry Rolen. 2011-07-20. Integrality Properties of the CM-values of Certain Weak Maass Forms. https://arxiv.org/abs/1107.4114

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