English

Notes on certain binomial harmonic sums of Sun's type

Number Theory 2026-03-10 v2 High Energy Physics - Theory Classical Analysis and ODEs

Abstract

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 Yg+1=(1X)gX(1tX)Y^{ g+1}=(1-X)^{ g}X(1-t X) of positive genera g{1,2,3,5} g\in\{1,2,3,5\}.

Keywords

Cite

@article{arxiv.2503.05599,
  title  = {Notes on certain binomial harmonic sums of Sun's type},
  author = {Yajun Zhou},
  journal= {arXiv preprint arXiv:2503.05599},
  year   = {2026}
}

Comments

47 pages, 6 tables. Accepted version

R2 v1 2026-06-28T22:11:01.728Z