Selberg Integral over Local Fields

Selberg introduced his beautiful integral formula in 1944, see [Sel]. Evans [E1] conjectured a finite field analog of Selberg integral formula in 1980. And Anderson [An] proved a major case of it in 1981 and his ideas was used to obtained the complete result [E2]. On the other hand, Aomoto [Ao] proved an analog of Selberg integral for complex field ${\mathbb{C}}$ in 1987. The purpose of the present paper is to formulate and prove Selberg integral formula for local fields of characteristic zero.