Depth-graded motivic multiple zeta values
Depth-graded motivic multiple zeta values
复制标题
深度分级动机多 zeta 值
作者：
F. Brown
我们研究的深度过滤多zeta值，对motivic伽罗瓦群的混合泰特动机超过$mathbb {Z}$和Grothendieck-Teichmüller群，以及它的关系，模块形式。利用$mathrm {SL} 2（mathbb {Z}）$的尖点形式的周期多项式，构造了线性化双洗牌方程解的一个显式李代数，给出了模zeta（2）$的多个zeta值与模下深度之间的所有恒等式的定性描述.我们制定了一个单一的猜想，这个李代数的同源性，这意味着由于布罗德赫斯特和Kreimer，Racinet，Zagier，和Drinfeld的结构上的多个zeta值和Grothendieck-Teichmüller李代数。
We study the depth filtration on multiple zeta values, on the motivic Galois group of mixed Tate motives over $mathbb {Z}$ and on the Grothendieck–Teichmüller group, and its relation to modular forms. Using period polynomials for cusp forms for $mathrm {SL} _2(mathbb {Z})$, we construct an explicit Lie algebra of solutions to the linearized double shuffle equations, which gives a conjectural description of all identities between multiple zeta values modulo $zeta (2)$ and modulo lower depth. We formulate a single conjecture about the homology of this Lie algebra which implies conjectures due to Broadhurst and Kreimer, Racinet, Zagier, and Drinfeld on the structure of multiple zeta values and on the Grothendieck–Teichmüller Lie algebra.