TY - JOUR
T1 - New functional equations of finite multiple polylogarithms
AU - Ono, Masataka
N1 - Funding Information:
This research was supported In part by KAKENHI 26247004, as well as the 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:
© 2020 Tohoku University, Mathematical Institute. All rights reserved.
PY - 2020/3
Y1 - 2020/3
N2 - We give a finite analogue of the well-known formula {equation presented) of multiple polylogarithms for any positive integer n by using the shuffle relation of finite multiple polylogarithms of Ono-Yamamoto type. Unlike the usual case, the terms regarded as error terms appear In this formula. As a corollary, we obtain "t ↔ 1 - t'' type new functional equations of finite multiple polylogarithms of Ono-Yamamoto type and Sakugawa-Seki type.
AB - We give a finite analogue of the well-known formula {equation presented) of multiple polylogarithms for any positive integer n by using the shuffle relation of finite multiple polylogarithms of Ono-Yamamoto type. Unlike the usual case, the terms regarded as error terms appear In this formula. As a corollary, we obtain "t ↔ 1 - t'' type new functional equations of finite multiple polylogarithms of Ono-Yamamoto type and Sakugawa-Seki type.
KW - Finite multiple polylogarithm
KW - Functional equation
KW - Shuffle relation
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U2 - 10.2748/tmj/1585101625
DO - 10.2748/tmj/1585101625
M3 - Article
AN - SCOPUS:85087461304
SN - 0040-8735
VL - 72
SP - 149
EP - 157
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
IS - 1
ER -