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On Zeta Functions and Families of Siegel Modular Form | | Alexei Panchishkin
; | | Date: |
11 Sep 2007 | | Abstract: | Let $p$ be a prime, and let $Gamma=Sp_g()$ be the Siegel modular group of
genus $g$. We study $p$-adic families of zeta functions and Siegel modular
forms. $L$-functions of Siegel modular forms are described in terms of motivic
$L$-functions attached to $Sp_g$, and their analytic properties are given.
Critical values for the spinor $L$-functions and $p$-adic constructions are
discussed. Rankin’s lemma of higher genus is established. A general conjecture
on a lifting from $ GSp_{2m} imes GSp_{2m}$ to $GSp_{4m}$ (of genus $g=4m$)
is formulated. Constructions of $p$-adic families of Siegel modular forms are
given using Ikeda-Miyawaki constructions. | | Source: | arXiv, 0709.1645 | | Services: | Forum | Review | PDF | Favorites | |
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