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.