SHINTANI FUNCTIONS AND AUTOMORPHIC L-FUNCTIONS FOR GL(n)

Dedicated to Professor Hideo Shimizu on his sixtieth birthday

抄録

We introduce certain special functions ("Shintani functions") on GL(n) over a non-Archimedean local field. We prove the uniqueness, existence and partial explicit formula of Shintani functions. We give several applications of these local results to the theory of automorphic L-functions for GL(n).