Weighted sum formula for multiple zeta values

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 (C) 2009 Elsevier Inc. All rights reserved.MathematicsSCI(E)8ARTICLE112747-276512