On variants of symmetric multiple zeta-star values and the cyclic sum formula

2020/01/12 by Minoru Hirose, Hideki Murahara, Hirose, Minoru +3 · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2001.03832

Abstract

The t-adic symmetric multiple zeta values were defined Jarossay, which have been studied as a real analogue of \boldsymbolp-adic finite multiple zeta values. In this paper, we consider the star analogues based on several regularization processes of multiple zeta-star values: harmonic regularization, shuffle regularization, and Kaneko-Yamamoto's type regularization. We also present the cyclic sum formula for t-adic symmetric multiple zeta(-star) values, which is the counterpart of that for \boldsymbolp-adic finite multiple zeta(-star) values obtained by Kawasaki. The proof uses our new relationship that connects the cyclic sum formula for t-adic symmetric multiple zeta-star values and that for the multiple zeta-star values.

Citations

• Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values

Cited by

• Truncated t-adic symmetric multiple zeta values and double shuffle relations
• Yamamoto's interpolation of finite multiple zeta and zeta-star values

Related

• On a lifting of t-adic symmetric multiple zeta values
• Truncated t-adic symmetric multiple zeta values and double shuffle relations
• On a generalization of the cyclic sum formula for finite multiple zeta and zeta-star values
• An algebraic proof of cyclic sum formula for multiple zeta values
• A combinatorial proof of the weighted sum formula for finite and symmetric multiple zeta(-star) values