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

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

2011-07-20

arxiv.org/abs/1107.4114v1

Mathematics

Number Theory

Scientific paper

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

Affiliated with

Also associated with

No associations

Rating

Integrality Properties of the CM-values of Certain Weak Maass Forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Integrality Properties of the CM-values of Certain Weak Maass Forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrality Properties of the CM-values of Certain Weak Maass Forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687095