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

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 $\zeta (2r)\zeta (2K+1-2r)$, $1\le r\le K-1$, in terms of the double zeta values $\zeta (2r,2K+1-2r)$, $1\le r\le K-1$ and $\zeta (2K+1)$.

arXiv comment11 pages