$q$-rious and $q$-riouser

TL;DR

This paper explores a mathematical problem posed by Dick Askey, highlighting its connections across analysis, number theory, and combinatorics, and demonstrating its significance in understanding these fields.

Contribution

It investigates a specific open problem by Dick Askey, revealing its interdisciplinary nature and contributing to the understanding of its underlying mathematical structures.

Findings

Unveiled connections between analysis, number theory, and combinatorics.

Provided insights into the structure of Askey's open problem.

Enhanced understanding of the problem's implications in multiple mathematical domains.

Abstract

Dick Askey is known not just for his beautiful mathematics and his many amazing theorems, but also for posing numerous interesting and important open problems. Dick being Dick, these problems are hardly ever isolated, and often intended to demonstrate the unity of analysis, number theory and combinatorics. We take the reader down the rabbit hole created by one such problem, published as Advanced Problem 6514 by the American Mathematical Monthly in April 1986.