Sun's Series via Cyclotomic Multiple Zeta Values

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• ISSN: 1815-0659
• Main Author: Zhou, Yajun
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212010
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Sun's Series via Cyclotomic Multiple Zeta Values. Yajun Zhou. SIGMA 19 (2023), 074, 20 pages

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 ∈ {4, 8, 12, 16, 24}, namely Goncharov's multiple polylogarit...