Properties of the zeros of the polynomials belonging to the q-Askey scheme

TL;DR

This paper investigates the zeros of polynomials in the q-Askey scheme, revealing new properties and Diophantine relations under specific parameter restrictions, advancing understanding of their mathematical structure.

Contribution

It introduces novel properties and Diophantine relations of zeros for q-Askey scheme polynomials, which were previously unknown.

Findings

New properties of zeros identified

Diophantine relations established for zeros

Parameter restrictions influence zero behavior

Abstract

In this paper we provide properties -- which are, to the best of our knowledge, new -- of the zeros of the polynomials belonging to the q-Askey scheme. These findings include Diophantine relations satisfied by these zeros when the parameters characterizing these polynomials are appropriately restricted.