ON FUNDAMENTAL FOURIER COEFFICIENTS of SIEGEL MODULAR FORMS

Bocherer, S and Das, S (2021) ON FUNDAMENTAL FOURIER COEFFICIENTS of SIEGEL MODULAR FORMS. In: Journal of the Institute of Mathematics of Jussieu .

PDF jou_ins_mat_jus_2021.pdf - Published Version Restricted to Registered users only Download (772kB) | Request a copy

Abstract

We prove that if F is a nonzero (possibly noncuspidal) vector-valued Siegel modular form of any degree, then it has infinitely many nonzero Fourier coefficients which are indexed by half-integral matrices having odd, square-free (and thus fundamental) discriminant. The proof uses an induction argument in the setting of vector-valued modular forms. Further, as an application of a variant of our result and complementing the work of A. Pollack, we show how to obtain an unconditional proof of the functional equation of the spinor L-function of a holomorphic cuspidal Siegel eigenform of degree 3 and level 1. © 2021 The Author(s). Published by Cambridge University Press.

Item Type:	Journal Article
Publication:	Journal of the Institute of Mathematics of Jussieu
Publisher:	Cambridge University Press
Additional Information:	The copyright for this article belongs to Cambridge University Press
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	23 Mar 2021 10:16
Last Modified:	23 Mar 2021 10:16
URI:	http://eprints.iisc.ac.in/id/eprint/68550

Actions (login required)

View Item