Algebraic A-hypergeometric Functions

TL;DR

This paper develops a combinatorial criterion to determine when A-hypergeometric systems possess a complete set of algebraic solutions, extending known criteria from one-variable hypergeometric functions to multivariable cases.

Contribution

It introduces a generalized combinatorial criterion for algebraicity of solutions in A-hypergeometric systems, broadening the understanding of their solution structure.

Findings

Established a criterion for algebraic solutions in A-hypergeometric systems

Generalized the interlacing criterion to multiple variables

Provided a method to identify algebraic solutions systematically

Abstract

We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differential equations has a full set of algebraic solutions or not. This criterion generalises the so-called interlacing criterion in the case of hypergeometric functions of one variable.