New Analytic Problems over Imaginary Quadratic Number Fields
by
Yoichi Motohashi
Nihon University, Tokyo, Japan

The aim of our talk is to ponder over the possibility of extending recent investigations on the fourth power moment of the Riemann zeta-function to imaginary quadratic number fields. We shall be led in a natural way to the spectral theory of the hyperbolic upper half-space, which if looked from our standpoint will turn out to be not a sheer counterpart of the 2-dimensional case but a fascinating subject raising genuinely new arithmetic and analytic problems.

Date received: February 4, 1999