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.