Vol. 14, No. 10, 2020

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Motivic multiple zeta values relative to $\mu_2$

Zhongyu Jin and Jiangtao Li

Vol. 14 (2020), No. 10, 2685–2712

We establish a short exact sequence about depth-graded motivic double zeta values of even weight relative to μ2. We find a basis for the depth-graded motivic double zeta values relative to μ2 of even weight and a basis for the depth-graded motivic triple zeta values relative to μ2 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.

multiple zeta values, period polynomial, mixed Tate motives
Mathematical Subject Classification 2010
Primary: 11F32
Secondary: 11F67
Received: 15 May 2019
Revised: 8 September 2019
Accepted: 13 June 2020
Published: 19 November 2020
Zhongyu Jin
School of Mathematical Sciences
Peking University
Jiangtao Li
Academy of Mathematics and Systems Science
Chinese Academy of Sciences