On Zeta Functions and Families of Siegel Modular Forms

الأصل · EN

Let p be a prime, and let Γ=() 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, 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 GSp₂ₘ × GSp₂ₘ to GSp₄ₘ (of genus g=4m) is formulated. Constructions of p-adic families of Siegel modular forms are given using Ikeda-Miyawaki constructions.