# Hypergeometric series, Barnes-type integrals, and Whittaker
functions

### Jennifer Taggart

### Mathematics Department

Dartmouth College

### Thursday, May 7, 1998

4:00 PM

### Room 102, Bradley Hall

The class one principal series Whittaker functions W_{n,a}(z) are central
to the Fourier development of automorphic forms on GL(n,R). Of particular
interest are the Mellin transforms M_{n,a}(s) of W_{n,a}(z). Until recently,
explicit formulas for M_{n,a}(s) had been deduced only for n <= 4. In
this talk, I will discuss joint work with Eric Stade that gives an explicit
formula for M_{5,a}(s) as a double integral of Barnes type. Further, we
use identities among hypergeometric series of type _4F_3(1) to show that,
for special values of s, this Mellin transform reduces to a ratio of gamma
functions.

This talk should be accessible to all.