Pairings of harmonic Maass-Jacobi forms involving special values of partial $L$-functions
Number Theory
2014-12-30 v1
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 -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.
Keywords
Cite
@article{arxiv.1412.8257,
title = {Pairings of harmonic Maass-Jacobi forms involving special values of partial $L$-functions},
author = {Dohoon Choi and Subong Lim},
journal= {arXiv preprint arXiv:1412.8257},
year = {2014}
}