Li Guo, Bingyong Xie
Published 2008-09-30Version 1
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.
Comments: 18 pages
Journal: J. Number Theory, 129 (2009) 2742 - 2765
Applications of shuffle product to restricted decomposition formulas for multiple zeta values
Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems
A note on evaluations of multiple zeta values
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