Maass-Jacobi Poincar\'e series and Mathieu Moonshine
Number Theory
2015-12-31 v6 Representation Theory
Abstract
Mathieu moonshine attaches a weak Jacobi form of weight zero and index one to each conjugacy class of the largest sporadic simple group of Mathieu. We introduce a modification of this assignment, whereby weak Jacobi forms are replaced by semi-holomorphic Maass-Jacobi forms of weight one and index two. We prove the convergence of some Maass-Jacobi Poincar\'e series of weight one, and then use these to characterize the semi-holomorphic Maass-Jacobi forms arising from the largest Mathieu group.
Cite
@article{arxiv.1409.4124,
title = {Maass-Jacobi Poincar\'e series and Mathieu Moonshine},
author = {Kathrin Bringmann and John Duncan and Larry Rolen},
journal= {arXiv preprint arXiv:1409.4124},
year = {2015}
}
Comments
27 pages, minor corrections