q-Algebraic Equations, their power series solutions, and the asymptotic behavior of their coefficients

TL;DR

This paper systematically studies q-algebraic equations, focusing on the existence, uniqueness, and regularity of solutions within Hahn series, emphasizing the asymptotic behavior of coefficients through theoretical results and algorithms.

Contribution

It provides a comprehensive analysis of q-algebraic equations, establishing conditions for solutions and exploring their asymptotic coefficient behavior using Hahn series.

Findings

Existence and uniqueness of solutions are established.

Regularity characterized by asymptotic coefficient behavior.

Algorithms for analyzing solutions are developed and illustrated.

Abstract

We give a systematic study of q-algebraic equations. The questions of existence, uniqueness and regularity of the solutions are solved in the space of grid-based Hahn series. The regularity is understood in terms of asymptotic behavior of coefficients, and is the main focus of this work. The results and algorithms are illustrated by many examples.