What question did this study set out to answer?

To derive a generating series expression for multiple zeta values with fixed weight, depth, and ending string.

June 13, 2026Open Access

Multiple zeta values ending with a fixed string

Puntos clave

To derive a generating series expression for multiple zeta values with fixed weight, depth, and ending string.
Derived the expression building on the Ohno-Zagier Theorem.
Identified bounded depth for sums of multiple zeta values.
Explored applications to double zeta values and interpolated evaluations.
Summed multiple zeta values of fixed parameters with depth bound ≤ total of fixed string values.
Provided new insights into evaluation methods for interpolated multiple zeta values.

Resumen

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 = (₁, , 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 has bounded depth ₁ + + ᵣ. We give some applications to evaluations of interpolated multiple zeta values, and to the generating series of double zeta values.

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