Sun's Series via Cyclotomic Multiple Zeta Values
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2023 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212010 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Sun's Series via Cyclotomic Multiple Zeta Values. Yajun Zhou. SIGMA 19 (2023), 074, 20 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862550494359060480 |
|---|---|
| author | Zhou, Yajun |
| author_facet | Zhou, Yajun |
| citation_txt | Sun's Series via Cyclotomic Multiple Zeta Values. Yajun Zhou. SIGMA 19 (2023), 074, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 polylogarithms evaluated at -th roots of unity.
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| first_indexed | 2026-03-13T04:00:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212010 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T04:00:07Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zhou, Yajun 2026-01-22T09:17:29Z 2023 Sun's Series via Cyclotomic Multiple Zeta Values. Yajun Zhou. SIGMA 19 (2023), 074, 20 pages 1815-0659 2020 Mathematics Subject Classification: 11M32; 11B65 arXiv:2306.04638 https://nasplib.isofts.kiev.ua/handle/123456789/212010 https://doi.org/10.3842/SIGMA.2023.074 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 polylogarithms evaluated at -th roots of unity. This research was supported in part by the Applied Mathematics Program within the Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4). I am truly grateful to Erik Panzer and Kam Cheong Au, whose software packages HyperInt and MultipleZetaValues furnished me with many concrete computational examples that inspired the present theoretical framework. My thanks are due to Zhi-Wei Sun for his thoughtful feedback on the initial draft of the manuscript, as well as the anonymous referees for their perceptive and constructive comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Sun's Series via Cyclotomic Multiple Zeta Values Article published earlier |
| spellingShingle | Sun's Series via Cyclotomic Multiple Zeta Values Zhou, Yajun |
| title | Sun's Series via Cyclotomic Multiple Zeta Values |
| title_full | Sun's Series via Cyclotomic Multiple Zeta Values |
| title_fullStr | Sun's Series via Cyclotomic Multiple Zeta Values |
| title_full_unstemmed | Sun's Series via Cyclotomic Multiple Zeta Values |
| title_short | Sun's Series via Cyclotomic Multiple Zeta Values |
| title_sort | sun's series via cyclotomic multiple zeta values |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212010 |
| work_keys_str_mv | AT zhouyajun sunsseriesviacyclotomicmultiplezetavalues |