论文标题
多个Zeta值及其Q-Analogues
Multiple zeta values and their q-analogues
论文作者
论文摘要
我们探讨了多个Zeta值（MZV）的理论及其$ Q $ - 属性的理论。多个Zeta值是满足理由的几个组合关系的数值。这些关系包括两个乘法关系，这些关系自然是由MZV与基础代数结构进行比较而自然产生的。我们通过以$ q \ to 1^ - $引入参数$ Q $来概括这些概念，我们返回到普通的MZVS。我们的特殊兴趣在于H. Bachmann最近引入的两个$ Q $型。他进一步猜测，这些$ q $ - 属性产生的$ \ mathbb {q} $ - 一致。在这篇论文中，我们建立了巴赫曼猜想的特定案例。
We explore the theory of multiple zeta values (MZVs) and some of their $q$-generalisations. Multiple zeta values are numerical quantities that satisfy several combinatorial relations over the rationals. These relations include two multiplicative relations, which arise naturally from comparison of the MZVs with an underlying algebraic structure. We generalise these concepts by introducing the parameter $q$ in such a way that as $q\to 1^-$ we return to the ordinary MZVs. Our special interest lies in two $q$-models recently introduced by H. Bachmann. He further conjectures that the $\mathbb{Q}$-spaces generated by these $q$-generalisations coincide. In this thesis we establish a particular case of Bachmann's conjecture.
