Multizeta Values for , Their Period Interpretation, and Relations between Them
Multizeta Values for , Their Period Interpretation, and Relations between Them
复制标题
的 Multizeta 值、它们的时期解释以及它们之间的关系
DOI：
10.1093/imrp/rnp010
复制
发表时间：
2009
影响因子：
1
通讯作者：
D. Thakur
中科院分区：
文献类型：
--
作者：
G. Anderson;D. Thakur
我们提供了一个周期的解释multizeta值（在功能ELD上下文中）在明确的张量幂的Carlitz动机（混合Carlitz-泰特t-动机）的迭代扩展。我们给出了这些多zeta值满足的组合相关关系的示例。最初由欧拉提出和研究的多zeta值，由于其在数学和数学物理研究中的出现，联系了不同的观点，近年来又重新引起人们的兴趣。它们自然地作为德林费尔德结合子的coecients出现，因此与量子群、结不变量和数学物理有联系。它们也出现在Grothendieck-Ihara程序中，通过投影线减去三点的基本群研究绝对伽罗瓦群，以及Tate motives，Feynman路径积分重正化等的迭代扩展的相关研究。我们将读者推荐给Broadhurst，Cartier，Deligne，Drinfeld，Ecalle，Furusho，Goncharov，Homan，
We provide a period interpretation for multizeta values (in the function eld context) in terms of explicit iterated extensions of tensor pow- ers of Carlitz motives (mixed Carlitz-Tate t-motives). We give examples of combinatorially involved relations that these multizeta values satisfy. The multizeta values introduced and studied originally by Euler have been pur- sued again recently with renewed interest because of their emergence in studies in mathematics and mathematical physics connecting diverse viewpoints. They occur naturally as coecients of the Drinfeld associator, and thus have connections to quantum groups, knot invariants and mathematical physics. They also occur in the Grothendieck-Ihara program to study the absolute Galois group through the funda- mental group of the projective line minus three points and related studies of iterated extensions of Tate motives, Feynman path integral renormalizations, etc. We re- fer the reader to papers on this subject by Broadhurst, Cartier, Deligne, Drinfeld, Ecalle, Furusho, Goncharov, Homan,