Representation Theory and Differential Equations : Proceedings of JMM Workshop on Representation Theory and Differential Equations,November 26-27,2016 Josai University

This is an announcement of a new result which is a generalization of Popa’s result in [Po]. Popa gives explicit formulas of Whittaker functions on GL(2,C) at the minimal K-types, and shows that the local zeta integrals for GL(2,C) defined from some Whittaker functions are equal to the associated L-factors. In this article, we will give explicit formulas of Whittaker functions on GL(2,C) at all K-types, and show that the local zeta integrals for GL(2,C) × GL(2,C) defined from some Whittaker functions are equal to the associated L-factors. Proofs will appear elsewhere