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Dilogarithm identities after Bridgeman

Part of: Deformations of analytic structures Elementary number theory Computational number theory

Published online by Cambridge University Press:  03 March 2022

PRADTHANA JAIPONG ,
MONG LUNG LANG ,
SER PEOW TAN  and
MING HONG TEE
PRADTHANA JAIPONG
Affiliation:
Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand 50200. e-mail: pradthana.j@cmu.ac.th
MONG LUNG LANG
Affiliation:
Singapore. e-mail: lang2to46@gmail.com
SER PEOW TAN
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119076. e-mails: mattansp@nus.edu.sg, asptan@gmail.com, e0174864@u.nus.edu
MING HONG TEE
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119076. e-mails: mattansp@nus.edu.sg, asptan@gmail.com, e0174864@u.nus.edu
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Abstract

Following Bridgeman, we demonstrate several families of infinite dilogarithm identities associated with Fibonacci numbers, Lucas numbers, convergents of continued fractions of even periods, and terms arising from various recurrence relations.

MSC classification

Primary: 11A55: Continued fractions 11Y70: Values of arithmetic functions; tables 32G15: Moduli of Riemann surfaces, Teichmüller theory
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 174 , Issue 1 , January 2023 , pp. 1 - 23
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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Footnotes

†

Supported by Chiang Mai University.

‡

Partially supported by the National University of Singapore academic research grant R-146-000-289-114.

§

The first and third author are grateful to the Temasek foundation for support.

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