On the Potential Function of the Colored Jones Polynomial and the AJ conjecture

TL;DR

This paper explores the relationship between the $A$-polynomial, the colored Jones polynomial, and the AJ conjecture through the lens of the potential function, aiming to unify these conjectures.

Contribution

It introduces a new perspective by connecting the $A$-polynomial and the AJ conjecture via the parametrized potential function.

Findings

Establishes a link between the potential function and the $A$-polynomial.

Provides a unified framework for the AJ conjecture and the $A$-polynomial.

Suggests new approaches for verifying the conjectures.

Abstract

The $A$-polynomial is conjectured to be obtained from the potential function of the colored Jones polynomial by elimination. The AJ conjecture also implies the relationship between the $A$-polynomial and the colored Jones polynomial. In this paper, we connect these conjectures from the perspective of the parametrized potential function.