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

Dohoon Choi, Subong Lim

Research output: Contribution to journalArticle

Abstract

We prove that, for a given Jacobi integral F, there is a harmonic Maass-Jacobi form such that its holomorphic part is F, and that the converse is also true. As an application, we construct a pairing between two Jacobi integrals that 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 an analogue of the Haberland formula of elliptic modular forms for Jacobi forms.

Original languageEnglish
Pages (from-to)442-467
Number of pages26
JournalJournal of Number Theory
Volume157
DOIs
Publication statusPublished - 2015 Dec 1
Externally publishedYes

Fingerprint

Harmonic Forms
Jacobi Forms
L-function
Pairing
Partial
Cusp Form
Jacobi
Skew
Modular Forms
Scalar, inner or dot product
Converse
Analogue

Keywords

  • Haberland formula
  • Harmonic Maass-Jacobi form
  • Jacobi integral
  • Primary
  • Secondary

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Pairings of harmonic Maass-Jacobi forms involving special values of partial L-functions. / Choi, Dohoon; Lim, Subong.

In: Journal of Number Theory, Vol. 157, 01.12.2015, p. 442-467.

Research output: Contribution to journalArticle

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