On a conjecture of Kaneko and Ohno

Abstract

Let $X_0^{\star }(k,n,s)$ denote the sum of all multiple zeta-star values of weight $k$, depth $n$ and height $s$. Kaneko and Ohno conjecture that for any positive integers $m,n,s$ with $m,n⩾s$, the difference $(-1{)}^m{X}_0^{\star }(m+n+1,n+1,s)-(-1{)}^n{X}_0^{\star }(m+n+1,m+1,s)$ can be expressed as a polynomial of zeta values with rational coefficients. We give a proof of this conjecture in this paper.

10 pages

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