Abstract
The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier. Recently a weighted form of Euler's formula was obtained by Ohno and Zudilin. We generalize it to a weighted sum formula for multiple zeta values of all dimensions.
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