Multiple zeta values ending with a fixed string

Abstract

We give a generating series expression for the sum of all multiple zeta values of a fixed weight, depth, and height, which end with a given string $\vec{\ell }=({\ell }_1,\dots ,{\ell }_r)$; this builds upon the proof of the Ohno-Zagier Theorem. In particular, the sum of all multiple zeta values of fixed weight, depth and ending with $\vec{\ell }$ has bounded depth $\le {\ell }_1+\cdots +{\ell }_r$. We give some applications to evaluations of interpolated multiple zeta values, and to the generating series of double zeta values.

12 pages