Notes on certain binomial harmonic sums of Sun's type
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908870909100032 |
|---|---|
| author | Zhou, Yajun |
| author_facet | Zhou, Yajun |
| contents | We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by interpreting them as automorphic objects on the moduli spaces for Legendre curves $Y^{ g+1}=(1-X)^{ g}X(1-t X)$ of positive genera $ g\in\{1,2,3,5\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on certain binomial harmonic sums of Sun's type Zhou, Yajun Number Theory High Energy Physics - Theory Classical Analysis and ODEs 11F67, 11M06, 33C05 We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by interpreting them as automorphic objects on the moduli spaces for Legendre curves $Y^{ g+1}=(1-X)^{ g}X(1-t X)$ of positive genera $ g\in\{1,2,3,5\}$. |
| title | Notes on certain binomial harmonic sums of Sun's type |
| topic | Number Theory High Energy Physics - Theory Classical Analysis and ODEs 11F67, 11M06, 33C05 |
| url | https://arxiv.org/abs/2503.05599 |