A class of relations among multiple zeta values

A class of relations among multiple zeta values (2009)

Cached

Download Links

by Gaku Kawashima

Citations:

BibTeX

@MISC{Kawashima09aclass,
    author = {Gaku Kawashima},
    title = {A class of relations among multiple zeta values},
    year = {2009}
}

Bookmark

OpenURL

Abstract

We prove a new class of relations among multiple zeta values (MZV’s) which contains Ohno’s relation. We also give the formula for the maximal number of independent MZV’s of fixed weight, under our new relations. To derive our formula for MZV’s, we consider the Newton series whose values at non-negative integers are finite multiple harmonic sums. keywords multiple zeta value, the Newton series, Ohno’s relation 1

Citations

482	Combinatorics on Words - Lothaire - 1983
189	Free Lie algebras - Reutenauer - 1993
113	C.Reutenauer, Duality between Quasi-Symmetric Functions and the Solomon Descent algebra - Malvenuto - 1995
108	The algebra of multiple harmonic series - Hoffman - 1997
61	Values of zeta functions and their applications - Zagier
54	The Calculus of Finite Differences - Milne-Thomson - 1951
41	A generalization of the duality and sum formulas on the multiple zeta values - Ohno - 1999
36	Meditationes circa singulare serierum genus, Novi Comm - Euler - 1927
26	Relations of multiple zeta values and their algebraic expression - Hoffman, Ohno
18	Harmonic sums and Mellin transforms up to two-loop order, Phys - Blümlein, Kurth - 1999
11	Quasi-symmetric functions and mod p multiple harmonic sums, preprint math.NT/0401319 - Hoffman
8	Cyclic sum of multiple zeta values - Ohno, Wakabayashi
6	Derivation relations and regularized double shuffle relations of multiple zeta values - Ihara, Kaneko, et al.
6	On an extension of the derivation relation for multiple zeta values - Kaneko - 2007
3	On extended derivation relations for multiple zeta values, submitted - Tanaka
1	Algebraic setup of non-strict multiple zeta values, preprint arXiv:0711.0252 - Muneta