Tomoya Machide
Published 2011-12-12Version 1
A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and depth. Recently weighted sum formulas, which are weighted analogues of the sum formula, have been studied by many people. In this paper, we give two formulas of weighted sums with two parameters of multiple zeta values. As applications of the formulas, we find some linear combinations of multiple zeta values which can be expressed as polynomials of usual zeta values with coeffcients in the rational polynomial ring generated by the two parameters, and obtain some identities for weighted sums of multiple zeta values of small depths.
Comments: 14 pages
Journal: Int. J. Number Theory 8 (2012), 1903-1921
On generalizations of the sum formula for multiple zeta values
A cyclic analogue of multiple zeta values
Iterated integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty,z\}$ and a class of relations among multiple zeta values
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