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On convolutions of Siegel modular forms

✍ Scribed by Özlem Imamoğlu; Yves Martin

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
289 KB
Volume
273
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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)

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