The Graphs of Quantum Dilogarithm

2011/08/26 by Ivan Chi Ho Ip, Ivan Chi-Ho Ip, Ip, Ivan Chi-Ho · 2 citations
Engineering · Mathematics · #20G42 #33E #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Biology #Computer science #Discrete mathematics #Engineering #FOS: Mathematics #Function (biology) #Limiting #Mathematics #Physics #Process (computing) #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum mechanics #Representation Theory (math.RT) #math.QA #math.RT #msc:20G42 #msc:33E

paper · pdf · doi:10.48550/arxiv.1108.5376

published in arXiv (Cornell University) (Cornell University) · 27 pages, 24 figures, fixed typos and references

openalex publication_date 2011/08/26 · arxiv created 2011/12/01 · arxiv updated 2011/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)→ Γ(z) as b→ 0. We also survey the relations of G_b(z) with different variants of the quantum dilogarithm function.

Citations

• The pentagon relation for the quantum dilogarithm and quantized M_0,5
• Liouville bootstrap via harmonic analysis on a noncompact quantum group

Related

• A remark on zeta functions of finite graphs via quantum walks
• Quantum Graphs via Exercises
• Numerical Computation of Non-Equilateral Quantum Graph Spectra
• Recent results of quantum ergodicity on graphs and further investigation
• A zeta function related to the transition matrix of the discrete-time quantum walk on a graph