On a conjecture of Kaneko and Ohno

Original · EN

Let X₀⋆(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)ᵐX₀⋆(m+n+1,n+1,s)-(-1)ⁿX₀⋆(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.