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arXiv · 2503.05599

Notes on certain binomial harmonic sums of Sun's type

Yajun Zhou
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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 $Y^{ g+1}=(1-X)^{ g}X(1-t X)$ of positive genera $ g\in\{1,2,3,5\}$.

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Yajun Zhou. 2025-03-07. Notes on certain binomial harmonic sums of Sun's type. https://doi.org/10.1007/s11139-026-01333-5

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