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

Masanobu Kaneko; Shuji Yamamoto

doi:10.1007/s00029-018-0400-8

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

Masanobu Kaneko, Shuji Yamamoto

Graduate School of Science and Technology

Research output: Contribution to journal › Article › peer-review

7 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 language	English
Pages (from-to)	2499-2521
Number of pages	23
Journal	Selecta Mathematica, New Series
Volume	24
Issue number	3
DOIs	https://doi.org/10.1007/s00029-018-0400-8
Publication status	Published - 2018 Jul 1

Keywords

Kawashima’s relation
Multiple zeta values
Multiple zeta-star values
Regularized double shuffle relation

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)

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10.1007/s00029-018-0400-8

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