Notes on $$2D$$ $$\mathbb{F}_p$$-Selberg Integrals

We prove a two-dimensional $$\mathbb{F}_p$$ -Selberg integral formula, in which the two-dimensional $$\mathbb{F}_p$$ -Selberg integral $$\overline S(a,b,c;l_1,l_2)$$ depends on positive integer parameters $$a,b,c$$ , $$l_1,l_2$$ and is an element of the finite field $$\mathbb{F}_p$$ with an odd prime number $$p$$ of elements. The formula is motivated by the analogy between multidimensional hypergeometric solutions of the KZ equations and polynomial solutions of the same equations reduced modulo $$p$$ .