On Zeta Functions and Families of Siegel Modular Forms
| dc.creator | Panchishkin, Alexei | |
| dc.date | 2007-09-11 | |
| dc.date.accessioned | 2026-07-07T08:28:47Z | |
| dc.date.available | 2026-07-07T08:28:47Z | |
| dc.description | Let $p$ be a prime, and let $Γ=\Sp_g(\Z)$ 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} \times 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. | |
| dc.description | in English and in Russian, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0709.1645 | |
| dc.identifier | http://arxiv.org/abs/0709.1645 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137742 | |
| dc.subject | Number Theory | |
| dc.subject | 11F46 | |
| dc.title | On Zeta Functions and Families of Siegel Modular Forms | |
| dc.type | text |