[based on joint work with Li Guo and Bin Zhang]
We apply to the study of exponential sums on lattice points in
convex rational polyhedral cones, the generalised algebraic approach of
Connes and Kreimer to perturbative quantum field theory. For this purpose
we equip the space of cones with a connected coalgebra structure.
The algebraic Birkhoff factorisation of Connes and Kreimer adapted and
generalised to this context then gives rise to a convolution factorisation
of exponential sums on lattice points in cones. We show that this
factorisation coincides with the classical Euler-Maclaurin formula
generalised to convex rational polyhedral cones by Berline and Vergne by
means of an interpolating holomorphic function.
We define renormalised conical zeta values at non-positive integers as the
Taylor coefficients at zero of the interpolating holomorphic function. When
restricted to Chen cones, this yields yet another way to renormalise
multiple zeta values at non-positive integers.
- Quantum Field Theory Seminar