Number Theory, Special Functions
I study automorphic forms, which lie at the intersection of number theory and harmonic analysis. In particular, I'm interested in the interplay between the Fourier theory of automorphic forms and the classical study of generalized Barnes integrals and hypergeometric series.
- On explicit integral formulas for GL(n, R)-Whittaker functions. Duke Math. Journal. 60 (1990), no. 2, 313-362.
- Hypergeometric series and Euler factors at infinity for L-functions on GL(3, R). American J. Math. 115 (1993), no. 2, 371-387.
- Generalized discrete Fourier transforms: the discrete Fourier-Riccati-Bessel transform, (with E. G. Layton). Computer Phys. Comm. 85 (1995), no. 3, 336-373.
- Mellin transforms of GL(n, R) Whittaker functions. American J. Math. 123 (2001), no. 1, 121-161.
- New formulas for GL(n, R) Whittaker functions, (with Taku Ishii). J. Funct. Anal. 244 (2007), no. 1, 289-314.