A new integral–series identity of multiple zeta values and regularizations

Masanobu Kaneko, Shuji Yamamoto

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We present a new “integral = series” type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear relations of multiple zeta values over Q. We also establish the regularization theorem for multiple zeta-star values, which too is equivalent to our new identity. A connection to Kawashima’s relation is discussed as well.

Original languageEnglish
Pages (from-to)2499-2521
Number of pages23
JournalSelecta Mathematica, New Series
Volume24
Issue number3
DOIs
Publication statusPublished - Jul 1 2018

Fingerprint

Multiple zeta Values
Regularization
theorems
Linear Relation
Theorem
Star
stars
Series

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

A new integral–series identity of multiple zeta values and regularizations. / Kaneko, Masanobu; Yamamoto, Shuji.

In: Selecta Mathematica, New Series, Vol. 24, No. 3, 01.07.2018, p. 2499-2521.

Research output: Contribution to journalArticle

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