Sun's Series via Cyclotomic Multiple Zeta Values
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∈\4,8,12,16,24\, namely Goncharov's multiple polylogarithms evaluated at N-th roots of unity.
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