[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.