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arXiv · 1412.8257

Pairings of harmonic Maass-Jacobi forms involving special values of partial $L$-functions

Dohoon Choi·Subong Lim
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Abstract

In this paper, considering the Eichler-Shimura cohomology theory for Jacobi forms, we study connections between harmonic Maass-Jacobi forms and Jacobi integrals. As an application we study a pairing between two Jacobi integrals, which is defined by special values of partial $L$-functions of skew-holomorphic Jacobi cusp forms. We obtain connections between this pairing and the Petersson inner product for skew-holomorphic Jacobi cusp forms. This result can be considered as analogue of Haberland formula of elliptic modular forms for Jacobi forms.

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Dohoon Choi, Subong Lim. 2014-12-29. Pairings of harmonic Maass-Jacobi forms involving special values of partial $L$-functions. https://arxiv.org/abs/1412.8257

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