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Petersson norms of not necessarily cuspidal Jacobi modular forms and applications

Boecherer, Siegfried and Das, Soumya (2018) Petersson norms of not necessarily cuspidal Jacobi modular forms and applications. In: ADVANCES IN MATHEMATICS, 336 . pp. 335-376.

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Official URL: http://dx.doi.org/ 10.1016/j.aim.2018.07.033

Abstract

We extend the usual notion of Petersson inner product on the space of cuspidal Jacobi forms to include non-cuspidal forms as well. This is done by examining carefully the relation between certain ``growth-killing'' invariant differential operators on H-2 and those on H-1 x C (here H-n denotes the Siegel upper half space of degree n). As applications, we can understand better the growth of Petersson norms of Fourier Jacobi coefficients of Klingen Eisenstein series, which in turn has applications to finer issues about representation numbers of quadratic forms; and as a by-product we also show that any Siegel modular form of degree 2 is determined by its `fundamental' Fourier coefficients. (C) 2018 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belong to ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Keywords: Petersson norm; Invariant differential operators; Representation numbers
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 26 Sep 2018 15:27
Last Modified: 26 Sep 2018 15:27
URI: http://eprints.iisc.ac.in/id/eprint/60728

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