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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 074, 20 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.074 (Mi sigma1969) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Sun's Series via Cyclotomic Multiple Zeta Values

Yajun Zhouab

a Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, NJ 08544, USA
b Academy of Advanced Interdisciplinary Studies (AAIS), Peking University, Beijing 100871, P.R. China
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DOI: https://doi.org/10.3842/SIGMA.2023.074
URL: https://www.emis.de/journals/SIGMA/2023/074/
Abstract: We prove and generalize several recent conjectures of Z.-W. Sun surrounding binomial coefficients and harmonic numbers. We show that Sun's series and their analogs can be represented as cyclotomic multiple zeta values of levels $N\in\{4,8,12,16,24\} $, namely Goncharov's multiple polylogarithms evaluated at $N $-th roots of unity.
Keywords: Sun's series, binomial coefficients, harmonic numbers, cyclotomic multiple zeta values.
Received: June 13, 2023; in final form September 29, 2023; Published online October 12, 2023
Bibliographic databases:
Document Type: Article
MSC: 11M32, 11B65
Language: English
Citation: Yajun Zhou, “Sun's Series via Cyclotomic Multiple Zeta Values”, SIGMA, 19 (2023), 074, 20 pp.
Citation in format AMSBIB
\Bibitem{Zho23}
\by Yajun~Zhou
\paper Sun's Series via Cyclotomic Multiple Zeta Values
\jour SIGMA
\yr 2023
\vol 19
\papernumber 074
\totalpages 20
\mathnet{http://mi.mathnet.ru/sigma1969}
\crossref{https://doi.org/10.3842/SIGMA.2023.074}
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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