The Graphs of Quantum Dilogarithm

TL;DR

This paper visualizes the quantum dilogarithm function's behavior using complex coloring, explores its limits, and surveys its relations with other variants, providing insights into its analytic and asymptotic properties.

Contribution

It introduces a visual approach to understanding the quantum dilogarithm and details its limiting behavior and relations with other functions.

Findings

Visualization of $G_b(z)$ and its asymptotic behavior

Demonstration of the limit $G_b(z) o \Gamma(z)$ as $b o 0$

Survey of relations with other quantum dilogarithm variants

Abstract

Using the complex coloring method, we present the graphs of the quantum dilogarithm function $G_b(z)$ and visualize its analytic and asymptotic behaviours. In particular we demonstrate the limiting process when the modified $G_b(z)\to \Gamma(z)$ as $b\to 0$. We also survey the relations of $G_b(z)$ with different variants of the quantum dilogarithm function.