OHNO-TYPE RELATION FOR FINITE MULTIPLE ZETA VALUES
نویسندگان
چکیده
منابع مشابه
Ju n 20 01 New Approach to Ohno Relation for Multiple Zeta Values
The weight and the depth of ζ(k1, . . . , km) are k1 + · · ·+ km and m, respectively. Recently, MZVs have been studied extensively in number theory [Go, Z], knot theory [LM], mirror symmetry [H3] and perturbative quantum field theory [Kr]. Many relations of MZVs, for example Hoffman’s relation [H1], the duality formula [Z], the sum formula [Gr], Le-Murakami’s relation [LM] and the cyclic sum fo...
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 کاملA 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 کاملOn a Reciprocity Law for Finite Multiple Zeta Values
Abstract. It was shown in [7, 9] that harmonic numbers satisfy certain reciprocity relations, which are in particular useful for the analysis of the quickselect algorithm. The aim of this work is to show that a reciprocity relation from [7, 9] can be generalized to finite variants of multiple zeta values, involving a finite variant of the shuffle identity for multiple zeta values. We present th...
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: Kyushu Journal of Mathematics
سال: 2018
ISSN: 1340-6116,1883-2032
DOI: 10.2206/kyushujm.72.277