Solutions of KZ differential equations modulo $p$

TL;DR

This paper constructs polynomial solutions to KZ differential equations over finite fields, serving as analogs to hypergeometric solutions, and explores their properties in the modular setting.

Contribution

It introduces a novel method for solving KZ equations modulo p, extending hypergeometric solutions to finite fields.

Findings

Polynomial solutions over F_p are explicitly constructed.

The solutions generalize classical hypergeometric functions to finite fields.

Potential applications in number theory and algebraic geometry.

Abstract

We construct polynomial solutions of the KZ differential equations over a finite field $F_p$ as analogs of hypergeometric solutions.