Sun's Series via Cyclotomic Multiple Zeta Values

Yajun Zhou

doi:10.3842/sigma.2023.074

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arXiv · 2306.04638

Sun's Series via Cyclotomic Multiple Zeta Values

Yajun Zhou

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Abstract

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 $N\in\{4,8,12,16,24\}$, namely Goncharov's multiple polylogarithms evaluated at $N$-th roots of unity.

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Yajun Zhou. 2023-06-07. Sun's Series via Cyclotomic Multiple Zeta Values. https://doi.org/10.3842/sigma.2023.074

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