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 𝑁 ∈ {4, 8, 12, 16, 24}, namely Goncharov's multiple polylogari...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2023 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2023
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212010 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 ∈ {4, 8, 12, 16, 24}, namely Goncharov's multiple polylogarithms evaluated at 𝑁-th roots of unity.
|
|---|---|
| ISSN: | 1815-0659 |