A generalization of Ohnoʼs relation for multiple zeta values
نویسندگان
چکیده
منابع مشابه
A generalization of Ohno’s relation for multiple zeta values
In the present paper, we prove that certain parametrized multiple series satisfy the same relation as Ohno’s relation for multiple zeta values. This result gives us a generalization of Ohno’s relation for multiple zeta values. By virtue of this generalization, we obtain a certain equivalence between the above relation among the parametrized multiple series and a subfamily of the relation. As ap...
متن کاملAn exotic shuffle relation for multiple zeta values
In this short note we will provide a new proof of the following exotic shuffle relation of multiple zeta values: ζ({2}x{3, 1}) = ( 2n+m m ) π (2n+ 1) · (4n+ 2m+ 1)! . This was proved by Zagier when n = 0, by Broadhurst when m = 0, and by Borwein, Bradley, and Broadhurst when m = 1. In general this was proved by Bowman and Bradley. Our new idea is to use the method of Borwein et al. to reduce th...
متن کاملOn the Quasi-derivation Relation for Multiple Zeta Values
Recently, Masanobu Kaneko introduced a conjecture on an extension of the derivation relation for multiple zeta values. The goal of the present paper is to present a proof of this conjecture by reducing it to a class of relations for multiple zeta values studied by Kawashima. In addition, some algebraic aspects of the quasi-derivation operator ∂ (c) n on Q〈x, y〉, which was defined by modeling a ...
متن کاملAspectsof Multiple Zeta Values
Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuue product rule allows the possibility of a combi-natorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with ...
متن کاملMultiple Zeta Values
for any collection of positive integers s1, s2, . . . , sl. By definition, Lis(1) = ζ(s), s ∈ Z, s1 ≥ 2, s2 ≥ 1, . . . , sl ≥ 1. (4.2) Taking, as before for multiple zeta values, Lixs(z) := Lis(z), Li1(z) := 1, (4.3) let us extend action of the map Li : w 7→ Liw(z) by linearity on the graded algebra H (not H, since multi-indices are coded by words in H). Lemma 4.1. Let w ∈ H be an arbitrary non...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2012
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2011.09.005