Zeta-function on a generalized cone (Q1381929)

The authors derive explicit analytic expressions for the zeta function of a Laplace operator acting on functions (massless scalar fields) in a generalized cone \(\mathbb{R}^+\times M^N\) with an arbitrary smooth base, following Cheeger's approach. 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 regularization does not ``regularize'' and a further substraction is required for the related one-loop effective potential.