  The analytic properties of the zeta-function for a Laplace operator on a
generalised cone are studied in some detail using the Cheeger's approach and
explicit expressions are given. In the compact case, the zeta-function of the
Laplace operator turns out to be singular at the origin. As a result, strictly
speaking, the zeta-function regularisation does not ``regularise'' and a
further subtraction is required for the related one-loop effective potential.
