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

Addendum to arXiv:2210.17243v3, verifying and generalizing Conjectures 2.2-2.8 in arXiv:2210.07238v8

References in corpus (6)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Series with summands involving harmonic numbers
• On two conjectures of Sun concerning Apéry-like series
• Iterated Integrals and Multiple Polylogarithm at Algebraic Arguments
• Sun's Three Conjectures on Apéry-like Sums Involving Harmonic Numbers
• A Note on Sun's Conjectures on Apéry-like Sums Involving Lucas Sequences and Harmonic Numbers

Cited by in corpus (2)

• New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values
• Hyper-Mahler measures via Goncharov-Deligne cyclotomy