On integral kernels for Dirichlet series associated to Jacobi forms
type: Item
instance of: scholarly article
title: On integral kernels for Dirichlet series associated to Jacobi forms
zbMATH Open document ID: 1298.11039
author: Yves Martin
publication date: 2014-08-08T00:00:00Z
full work available at URL: http://hdl.handle.net/10533/135125
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 6327927
zbMATH Keywords: Jacobi forms
zbMATH Keywords: Dirichlet series
zbMATH Keywords: Mellin transform
zbMATH Keywords: Fourier coefficients
MaRDI profile type: Publication
OpenAlex ID: W2169949854
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DOI: 10.1112/JLMS/JDU016
published in: Journal of the London Mathematical Society. Second Series
review text: Every Jacobi cusp form of weight \(k\) and index \(m\) over the semidirect product of \(\mathrm{SL}_2(\mathbb Z)\) and \( \mathbb Z^2\) corresponds to \(2m\) Dirichlet series constructed with its Fourier coefficients. This connection is generally described by a variation of the Mellin transform. The author describes a set of integral kernels which yield the \(2m\) Dirichlet series via the Petersson inner-product. It is shown that those kernels are Jacobi cusp forms and they are expressed in terms of Jacobi Poincaré series. Finally, a new proof is given of the analytic continuation and functional equations satisfied by these Dirichlet series.
reviewed by: Steven T. Dougherty
description: scientific article; zbMATH DE number 6327927