  Conical zeta values associated with rational convex polyhedral cones
generalise multiple zeta values. We renormalise conical zeta values at poles by
means of a generalisation of Connes and Kreimer's Algebraic Birkhoff
Factorisation. This paper serves as a motivation for and an application of this
generalised renormalisation scheme. The latter also yields an Euler-Maclaurin
formula on rational convex polyhedral lattice cones which relates exponential
sums to exponential integrals. When restricted to Chen cones, it reduces to
Connes and Kreimer's Algebraic Birkhoff Decomposition for maps with values in
the algebra of ordinary meromorphic functions in one variable.
