On zeta functions and families of Siegel modular forms |
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Authors: | Alexei Panchishkin |
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Institution: | 1.Institut Fourier, CNRS UMR 5582,Université Grenoble 1,Saint-Martin d’Hères cedex,France |
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Abstract: | Let p be a prime, and let
G = \textS\textpg( \mathbbZ ) \Gamma = {\text{S}}{{\text{p}}_g}\left( \mathbb{Z} \right) be the Siegel modular group of genus g. This paper is concerned with p-adic families of zeta functions and L-functions of Siegel modular forms; the latter are described in terms of motivic L-functions attached to Sp
g
; their analytic properties are given. Critical values for the spinor L-functions are discussed in relation to p-adic constructions. Rankin’s lemma of higher genus is established. A general conjecture on a lifting of modular forms from
GSp2m
× GSp2m
to GSp4m
(of genus g = 4 m) is formulated. Constructions of p-adic families of Siegel modular forms are given using Ikeda–Miyawaki constructions. |
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Keywords: | |
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