A Note on Fourier-Jacobi coefficients of Siegel modular forms
Sanoli Gun, Narasimha Kumar
TL;DR
This paper investigates the growth of Petersson norms of Fourier-Jacobi coefficients of Siegel cusp forms, providing sharper estimates than previous results, which enhances understanding of their asymptotic behavior.
Contribution
It offers improved bounds on the growth of Fourier-Jacobi coefficients' Petersson norms, refining earlier estimates by Kohnen.
Findings
Sharper growth estimates for Petersson norms
Enhanced understanding of Fourier-Jacobi coefficients
Refinement of previous asymptotic bounds
Abstract
Let F be a Siegel cusp form of weight k and genus n>1 with Fourier-Jacobi coefficients f_m. In this article, we estimate the growth of the Petersson norms of f_m, where m runs over an arithmetic progression. This result sharpens a recent result of Kohnen in [5].
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models