• Zeta functions of prehomogeneous vector spaces with coefficients related to periods of automorphic forms

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      https://www.ias.ac.in/article/fulltext/pmsc/104/01/0099-0135

    • Keywords

       

      Zeta function; prehomogeneous vector space; functional equation; automorphic form

    • Abstract

       

      The theory of zeta functions associated with prehomogeneous vector spaces (p.v. for short) provides us a unified approach to functional equations of a large class of zeta functions. However the general theory does not include zeta functions related to automorphic forms such as the HeckeL-functions and the standardL-functions of automorphic forms on GL(n), even though they can naturally be considered to be associated with p.v.’s. Our aim is to generalize the theory to zeta functions whose coefficients involve periods of automorphic forms, which include the zeta functions mentioned above.

      In this paper, we generalize the theory to p.v.’s with symmetric structure ofKε-type and prove the functional equation of zeta functions attached to automorphic forms with generic infinitesimal character. In another paper, we have studied the case where automorphic forms are given by matrix coefficients of irreducible unitary representations of compact groups.

    • Author Affiliations

       

      Fumihiro Sato1

      1. Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, Toshimaku, Tokyo - 171, Japan
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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