On the linear relations among parametrized multiple series
On the linear relations among parametrized multiple series
复制标题
论参数化多重级数之间的线性关系
DOI：
10.1007/s11139-022-00658-1
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Onozuka Tomokazu
中科院分区：
文献类型：
--
作者：
Hirose Minoru;Murahara Hideki;Onozuka Tomokazu
参数化多重级数是 Igarashi 引入的多重 zeta 值的概括。在这项工作中，我们完全确定了这些参数化多重序列之间的所有线性关系。具体来说，我们证明了以下两个陈述：多个 zeta 值的 Kawashima 关系的线性部分可以推广到参数化的多个序列；参数化多重级数之间的任何线性关系都可以写成川岛关系的线性部分的线性组合。
Parametrized multiple series are generalizations of the multiple zeta values introduced by Igarashi. In this work, we completely determine all the linear relations among these parametrized multiple series. Specifically, we prove the following two statements: the linear part of the Kawashima relation for multiple zeta values can be generalized to parametrized multiple series; any linear relations among the parametrized multiple series can be written as a linear combination of the linear part of the Kawashima relation.