A generating series is derived for the sum of multiple zeta values ending with a fixed string, implying the sum has depth bounded by the sum of the string entries.
Interpolation of multiple zeta and zeta-star values
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abstract
We define polynomials of one variable t whose values at t=0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the cyclic sum formula for these polynomials.
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Multiple zeta values ending with a fixed string
A generating series is derived for the sum of multiple zeta values ending with a fixed string, implying the sum has depth bounded by the sum of the string entries.