Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8354
Title: Non-vanishing of theta components of Jacobi forms with level and an application
Authors: ANAMBY, PRAMATH
Dept. of Mathematics
Keywords: Jacobi forms
theta components
Fourier coefficients
Siegel modular forms
non-vanishing
2023-DEC-WEEK3
TOC-DEC-2023
2023
Issue Date: Nov-2023
Publisher: World Scientific Publishing Co Pte Ltd
Citation: International Journal of Number Theory, 20(02), 549-564.
Abstract: We prove that a nonzero Jacobi form of level N (an odd integer) and square-free index m(1)m(2) with m1|N and (N, m(2)) = 1 has a nonzero theta component h mu with either (mu, 2m(1)m(2)) = 1 or (mu, 2m(1)m(2)) f (2)m(2). As an application, we prove that a nonzero Siegel cusp form F of degree 2 and an odd level N in the Atkin-Lehner type newspace is determined by fundamental Fourier coefficients up to a divisor of N.
URI: https://doi.org/10.1142/S1793042124500295
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8354
ISSN: 1793-0421
1793-7310
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