Abstract
We present a new “integral (Formula presented.) 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 (Formula presented.). 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) | 1-23 |
| Number of pages | 23 |
| Journal | Selecta Mathematica, New Series |
| DOIs | |
| Publication status | Accepted/In press - 2018 Feb 16 |
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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)
Cite this
A new integral–series identity of multiple zeta values and regularizations. / Kaneko, Masanobu; Yamamoto, Shuji.
In: Selecta Mathematica, New Series, 16.02.2018, p. 1-23.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A new integral–series identity of multiple zeta values and regularizations
AU - Kaneko, Masanobu
AU - Yamamoto, Shuji
PY - 2018/2/16
Y1 - 2018/2/16
N2 - We present a new “integral (Formula presented.) 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 (Formula presented.). 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.
AB - We present a new “integral (Formula presented.) 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 (Formula presented.). 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.
KW - Kawashima’s relation
KW - Multiple zeta values
KW - Multiple zeta-star values
KW - Regularized double shuffle relation
UR - http://www.scopus.com/inward/record.url?scp=85042118825&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042118825&partnerID=8YFLogxK
U2 - 10.1007/s00029-018-0400-8
DO - 10.1007/s00029-018-0400-8
M3 - Article
AN - SCOPUS:85042118825
SP - 1
EP - 23
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
SN - 1022-1824
ER -