Taku Ishii, Chiba Institute of Technology
Archimedean zeta functions

The integral representation method is a powerful tool in the investigation of automorphic L-functions, and has been developed by many people. But to know deep arithmetic properties of L-functions, more detailed study of the archimedean and ramified parts of these zeta integrals seems to be necessary. We will discuss recent progress in the study of archimedean zeta integrals on GSp(2) by using a explicit formula of (generalized) Whittaker functions, especially the computation of gamma factors of spinor / standard L-functions to prove the global functional equations.