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On convolutions of Siegel modular forms
Author(s) -
Imamoğlu Özlem,
Martin Yves
Publication year - 2004
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310197
Subject(s) - mathematics , cusp (singularity) , cusp form , convolution (computer science) , siegel modular form , degree (music) , fourier series , pure mathematics , dirichlet distribution , mathematical analysis , modular form , geometry , physics , machine learning , artificial neural network , computer science , acoustics , boundary value problem
In this article we study a Rankin‐Selberg convolution of n complex variables for pairs of degree n Siegel cusp forms. We establish its analytic continuation to ℂ n , determine its functional equations and find its singular curves. Also, we introduce and get similar results for a convolution of degree n Jacobi cusp forms. Furthermore, we show how the relation of a Siegel cusp form and its Fourier‐Jacobi coefficients is reflected in a particular relation connecting the two convolutions studied in this paper. As a consequence, the Dirichlet series introduced by Kalinin [7] and Yamazaki [19] are obtained as particular cases. As another application we generalize to any degree the estimate on the size of Fourier coefficients given in [14]. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)