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Another Proof of Zagier's Matrix Conjecture Yawen Ma and Lee-Peng Teo
Department of Mathematics
Xiamen University Malaysia
Jalan Sunsuria, Bandar Sunsuria
43900, Sepang, Selangor
Malaysia
m1102439194@gmail.com
lpteo@xmu.edu.my

in

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