Multiple zeta values, conical zeta values and Euler-Maclaurine formula
主 题: Multiple zeta values, conical zeta values and Euler-Maclaurine formula
报告人: Professor Li Guo (Rutgers University-Newark and Lanzhou University)
时 间: 2013-10-25 14：00-15:00
地 点: 理科一号楼1114 （数学所活动）
Multiple zeta values (MZVs) are natural generalizations of the well-known Riemann values and play an important role in mathematics and mathematical physics. For example they are shown to span periods of mixed Tate motives and to give many Feynman integrals. In this talk we consider a geometric generalization of MZVs called conical zeta values, coming from convex cones. We study their double subdivision relations extending the fundamental double shuffle relation of MZVs. We further equip cones with a coalgebra structure and apply it to carry out a renormalization process for divergent conical zeta values. Finally this renormalization process is shown to be equivalent to the Euler-Maclaurine formula relating the enumeration of lattice points in a cone with the integration of the cone. This is joint work with Sylvie Paycha and Bin Zhang.