| 研究実績の概要 |
In the project "q-analogues of multiple zeta values and their applications in geometry" the connection of q-analogues and the study of a more broader class of q-series were studied. For this we (j.w. with Jan-Willem van Ittersum) introduced the notion of polynomial functions on partitions. The main result is that all these functions, which are given by the q-bracket of certain polynomials, are always give rise to q-analogues of multiple zeta values. In particular, we calculated the limit as q goes to 1. This connection allowed use to connect multiple zeta values to other functions on partitions, such as shifted symmetric functions. As an application we showed how these connections give rise to relations among multiple zeta values. In another project (j.w. Ulf Kuehn and Nils Matthes) we introduced the notion of the formal double Eisenstein space. This space can be seen as a generalization of the formal double zeta space introduced by Gangl-Kaneko-Zagier. We showed that any power series satisfying the Fay-idendity give rise to a realization of this space. In particular, the Kronecker-function gives rise to a realizatiom which is given in depth one by Eisensteins series and their derivatives.
|
