TY - JOUR
T1 - A new integral–series identity of multiple zeta values and regularizations
AU - Kaneko, Masanobu
AU - Yamamoto, Shuji
N1 - Funding Information:
Acknowledgements The authors are very grateful to the referee for his/her careful reading and valuable comments. This work was supported in part by JSPS KAKENHI Grant Nos. JP24224001, JP23340010, JP26247004, JP16H06336, as well as JSPS Joint Research Project with CNRS “Zeta functions of several variables and applications,” JSPS Core-to-Core program “Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory and Geometry” and the KiPAS program 2013–2018 of the Faculty of Science and Technology at Keio University.
Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - 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.
AB - 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.
KW - Kawashima’s relation
KW - Multiple zeta values
KW - Multiple zeta-star values
KW - Regularized double shuffle relation
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U2 - 10.1007/s00029-018-0400-8
DO - 10.1007/s00029-018-0400-8
M3 - Article
AN - SCOPUS:85042118825
VL - 24
SP - 2499
EP - 2521
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
SN - 1022-1824
IS - 3
ER -