论文标题
正则双Zeta值的模块化现象
Modular phenomena for regularized double zeta values
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {p}^{1} \ setMinus \ {0,1，\ infty \} $的正则动机迭代积分之间的线性关系，我们称之为正则化的动机双重Zeta值。动机多个Zeta值与模块化形式之间的一些神秘联系是已知的，例如Gangl - Kaneko-与完全奇怪的双重Zeta值和Ihara-takao关系的Zagier关系，用于分级动机的深度。在本文中，我们研究了所谓的不可接受的案例，并为正规动机双Zeta值提供了许多新的gangl-kaneko-zagier类型和ihara-taka-taka-taka-taka-taka型关系。具体而言，我们在某个正规化动机双Zeta值的家族中构建线性关系，从奇数周期的多项式形式的奇数索引形式的奇数多项式构建了整个模块化组的两个一致性亚组。这给出了第一个非琐碎的例子，即从模块化形式的多个Zeta值（或其类似物）之间的关系的构造，用于$ {\ rm sl} _ {2}（\ Mathbb {Z}）$以外的其他一致性子组。
In this paper, we investigate linear relations among regularized motivic iterated integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty\}$ of depth two, which we call regularized motivic double zeta values. Some mysterious connections between motivic multiple zeta values and modular forms are known, e.g. Gangl--Kaneko--Zagier relation for the totally odd double zeta values and Ihara--Takao relation for the depth graded motivic Lie algebra. In this paper, we investigate so-called non-admissible cases and give many new Gangl--Kaneko--Zagier type and Ihara--Takao type relations for regularized motivic double zeta values. Specifically, we construct linear relations among a certain family of regularized motivic double zeta values from odd period polynomials of modular forms for the unique index two congruence subgroup of the full modular group. This gives the first non trivial example of a construction of the relations among multiple zeta values (or their analogues) from modular forms for a congruence subgroup other than the ${\rm SL}_{2}(\mathbb{Z})$.
