The algebra of bi-brackets and regularized multiple Eisenstein series
The algebra of bi-brackets and regularized multiple Eisenstein series
复制标题
双括号代数和正则化多重爱森斯坦级数
DOI：
10.1016/j.jnt.2018.12.006
复制
发表时间：
2015
影响因子：
0.7
通讯作者：
Henrik Bachmann
中科院分区：
文献类型：
--
作者：
Henrik Bachmann
本文研究了一类称为双括号的q-级数的代数，它的系数由分拆上的加权和给出。这些级数结合了全模群的模形式理论以及多重zeta值理论（MZV），因为它们出现在正则化多重爱森斯坦级数的傅里叶展开中。使用共轭的分区，我们得到的双括号之间的线性关系，称为分区关系，自然产生两种不同的方式来表达类似于多个zeta值的填充和洗牌产品的两个双括号的产品。在最近的一项工作中，作者和K。Tasaka定义了（shuffle）正则化的多重爱森斯坦级数G，通过使用Goncharov引入的形式迭代积分上的余积的显式连接。这些满足shuffle乘积公式。将同样的概念应用于拟混洗代数上的余积，使我们能够定义（stuffle）正则化的多重爱森斯坦级数G满足stuffle积公式。我们证明了G和G都是由MZV和双括号的乘积的线性组合给出的。
We study the algebra of certain q-series, called bi-brackets, whose coefficients are given by weighted sums over partitions. These series incorporate the theory of modular forms for the full modular group as well as the theory of multiple zeta values (MZV) due to their appearance in the Fourier expansion of regularized multiple Eisenstein series. Using the conjugation of partitions we obtain linear relations between bi-brackets, called the partition relations, which yield naturally two different ways of expressing the product of two bi-brackets similar to the stuffle and shuffle product of multiple zeta values. In a recent work, the author and K. Tasaka defined (shuffle) regularized multiple Eisenstein series G⧢, by using an explicit connection to the coproduct on formal iterated integrals introduced by Goncharov. These satisfy the shuffle product formula. Applying the same concept for the coproduct on quasi-shuffle algebras enables us to define (stuffle) regularized multiple Eisenstein series G⁎ satisfying the stuffle product formula. We show that both G⧢ and G⁎ are given by linear combinations of products of MZV and bi-brackets.
DOI：
10.1007/978-3-030-37031-2_10
发表时间：
2014-12
期刊：
arXiv: Number Theory
影响因子：
--
作者：
Jianqiang Zhao
通讯作者：
Jianqiang Zhao
影响因子：
1.8
作者：
K. Ihara
通讯作者：
K. Ihara