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arXiv · 2106.15260

On Zagier's Conjecture About the Inverse of a Matrix Related to Double Zeta Values

Yawen Ma·Lee-Peng Teo
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Abstract

We prove a conjecture of Zagier about the inverse of a $(K-1)\times (K-1)$ matrix $A=A_{K}$ using elementary methods. This formula allows one to express the the product of single zeta values $\zeta(2r)\zeta(2K+1-2r)$, $1\leq r\leq K-1$, in terms of the double zeta values $\zeta(2r,2K+1-2r)$, $1\leq r\leq K-1$ and $\zeta(2K+1)$.

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Yawen Ma, Lee-Peng Teo. 2021-06-29. On Zagier's Conjecture About the Inverse of a Matrix Related to Double Zeta Values. https://arxiv.org/abs/2106.15260

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