The ${\mathbb{F}}_p$-Selberg Integral

Abstract

We prove an ${\mathbb{F}}_p$-Selberg integral formula, in which the ${\mathbb{F}}_p$-Selberg integral is an element of the finite field ${\mathbb{F}}_p$ with odd prime number $p$ of elements. The formula is motivated by analogy between multidimensional hypergeometric solutions of the KZ equations and polynomial solutions of the same equations reduced modulo $p$.

Latex, 19 pages, v2: references, remarks, formula (4.7) added