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arXiv · 1409.4124

Maass-Jacobi Poincar\'e series and Mathieu Moonshine

Kathrin Bringmann·John Duncan·Larry Rolen
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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.

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Kathrin Bringmann, John Duncan, Larry Rolen. 2014-09-15. Maass-Jacobi Poincar\'e series and Mathieu Moonshine. https://arxiv.org/abs/1409.4124

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