Weighted sum formula for multiple zeta values

Details Weighted sum formula for multiple zeta values Weighted sum formula for multiple zeta values

2008-09-30

arxiv.org/abs/0809.5110v1

J. Number Theory, 129 (2009) 2742 - 2765

Mathematics

Number Theory

18 pages

Scientific paper

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 independently. 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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