On analytic properties of the standard zeta function attached to a vector valued modular form

2021/08/14 by Stein, Oliver
#11F27 11F25 11F66 11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2108.06540

Abstract

We proof a Garrett-Böcherer decomposition of a vector valued Siegel Eisenstein series E_l,0² of genus 2 transforming with the Weil representation of Sp₂(ℤ) on the group ring ℂ[(L'/L)²]. We show that the standard zeta function associated to a vector valued common eigenform f for the Weil representation can be meromorphically continued to the whole s-plane and that it satisfies a functional equation. The proof is based on an integral representation of this zeta function in terms of f and E_l,0².

Related

• The standard L-function attached to a vector valued modular form
• The modularity of Siegel's zeta functions
• Projections of modular forms on Eisenstein series and its application to Siegel's formula
• Generalized L-functions related to the Riemann zeta function
• Local zeta factors and geometries under Spec Z