Motivic multiple zeta values relative to μ2

Jin, Zhongyu; Li, Jiangtao

doi:10.2140/ant.2020.14.2685

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Motivic multiple zeta values relative to $\mu_2$

Zhongyu Jin and Jiangtao Li

Vol. 14 (2020), No. 10, 2685–2712

DOI: 10.2140/ant.2020.14.2685

Abstract

We establish a short exact sequence about depth-graded motivic double zeta values of even weight relative to $μ_{2}$ . We find a basis for the depth-graded motivic double zeta values relative to $μ_{2}$ of even weight and a basis for the depth-graded motivic triple zeta values relative to $μ_{2}$ of odd weight. As an application of our main results, we prove Kaneko and Tasaka’s conjectures about the sum odd double zeta values and the classical double zeta values. We also prove an analogue of Kaneko and Tasaka’s conjecture in depth three. Finally, we formulate a conjecture which is related to sum odd multiple zeta values in higher depth.

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Keywords

multiple zeta values, period polynomial, mixed Tate motives

Mathematical Subject Classification 2010

Primary: 11F32

Secondary: 11F67

Milestones

Received: 15 May 2019

Revised: 8 September 2019

Accepted: 13 June 2020

Published: 19 November 2020

Authors

Zhongyu Jin
School of Mathematical Sciences Peking University Beijing China

Jiangtao Li
Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Vol. 14, No. 10, 2020