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

拟议的方案扩展研究了 “增强的”离散和，更具体地说，多个zeta值及其再正规化，增强有两种类型，-在组合方面， 与有根树相关联的分支ζ函数，其中梯形树对应于多个ζ函数;-在几何方面， 锥zeta函数与凸锥，与陈锥对应于多个zeta函数。将树结构所固有的分支过程转置到锥族中，得到分支锥，并利用分支Zeta函数所固有的锥结构研究了分支Zeta函数所产生的亚纯芽。 杆结构。

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.