The Graphs of Quantum Dilogarithm

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.

27 pages, 24 figures, fixed typos and references

References in corpus (2)

• Classical and Quantum Dilogarithm Identities
• The pentagon relation for the quantum dilogarithm and quantized M_{0,5}

Cited by in corpus (1)

• Representation of the Quantum Plane, its Quantum Double and Harmonic Analysis on $G{L}_q^{+}(2,R)$