Multiple zeta values vs. multiple zeta-star values

By K. Ihara, Jun Kajikawa, Yasuo Ohno, J. Okuda. 2011

63 citations recorded by the source corpus.

Abstract We discuss an algebraic connection between two kinds of multiple zeta values or their q -analogues: the ( q -)multiple zeta values and the ( q -)multiple zeta-star values. These two classes of values generate the same algebra, but in this paper, we show that the translation map between these two classes has a quite interesting algebraic property in a general setting, for example, the compatibility with the harmonic product. We also study several applications of the result.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/3f69d6d0e859b64c39630518bf818df8de2c8871

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Shuji Yamamoto
2. Michael E. Hoffman
3. K. Ihara
4. Don Zagier
5. F. Brown
6. A. Libgober
7. Masanobu Kaneko
8. Erik Panzer

In Discrete Mathematics and Combinatorics

1. Shuji Yamamoto
2. Michael E. Hoffman
3. K. Ihara
4. Don Zagier
5. F. Brown
6. Masanobu Kaneko
7. Li Guo
8. Bin Zhang

Citations in the corpus

• Quasi-shuffle products revisited (2016, methodology): “zjzk +(zi ⋄zj)zk +zi(zj ⋄zk) +zi ⋄zj ⋄zk and then ζ⋆(w) = ζ(Σ(w)). If we define analogously multiple q-zeta-star values ζ⋆ q (w), then ζ⋆ q(w) = ζq(Σ(w)). Important properties of Σ were established in [12], though some of the inductive proofs are tedious. Here we make use of two aspects of the theory”
• Evaluation of the multiple zeta values $\zeta(2,\dots,2,3,2,\dots,2)$ (2012, background): “The proof we have given of Theorem 4 and its corollary is analytic and works only for the multiple zeta-star values as real numbers, whereas the proof of Theorem 2 in [8] is algebraic and deduces the identity in question only from the double shuffle relations.”
• Interpolation of multiple zeta and zeta-star values (2012, methodology): “ Saito for helping to prove Proposition 3.4. INTERPOLATION OF MULTIPLE ZETA AND ZETA-STAR VALUES 3 2. Generalsetupfor harmonic algebra Here we recall the formulation of harmonic algebra introduced in [IKOO]. Let Abe a commutative Q-algebra, h1 a non-commutative A-algebra of polynomials of a letter s”