The Euler-Maclaurin formula and Birkhoff-Hopf factorisation: discretisation and quantisation Extension: Enhanced discrete sums; conical and branched zeta values

建议的方案扩展研究“增强”离散和之间的联系，更具体地说，多个zeta值及其重整化，增强是两种类型，在组合方面，分支zeta函数与根树相关联，阶梯树对应于多个zeta函数；在几何方面，圆锥zeta函数与凸锥相关联，陈锥对应于多个zeta函数。将树结构固有的分支过程转化为球果族，从而得到分支球果，并利用杆结构固有的圆锥结构研究由分支zeta函数产生的亚纯胚芽。

The proposed programme extension studies the connections between "enhanced" discrete sums, and more specifically multiple zeta values and their renormalisation, the enhancing being of two types,-on the combinatorial side, branched zeta functions associated with rooted trees, with ladder trees corresponding to multiple zeta functions;- on the geometric side, conical zeta functions associated with convex cones, with Chen cones corresponding to multiple zeta functions. The branching procedure inherent to the tree structure is transposed to families of cones, leading to branched cones and meromorphic germs arising from branched zeta functions are studied with the conical structure inherent to the pole structure.