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Motivic double zeta values of odd weight


For odd \(N\ge 5\), we establish a short exact sequence about motivic double zeta values \(\zeta ^{\mathfrak {m}}(r,N-r)\) with \(r\ge 3\) odd, \(N-r\ge 2\). From this we classify all the relations among depth-graded motivic double zeta values \(\zeta ^{\mathfrak {m}}(r,N-r)\) with \(r\ge 3\) odd, \(N-r\ge 2\). As a corollary, we confirm a conjecture of Zagier on the rank of a matrix which concerns relations among multiple zeta values of odd weight.

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The authors would like to express their sincere gratitude to the anonymous referee for his/her detailed comments to improve this paper.

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Correspondence to Jiangtao Li.

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Li, J., Liu, F. Motivic double zeta values of odd weight. manuscripta math. 166, 19–36 (2021).

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Mathematics Subject Classification

  • Primary 11F32
  • Secondary 11F67