Zeta function regularization in de Sitter space: The Minkowski limit

We study an integral representation for the zeta function of the one-loop effective potential for a minimally coupled massive scalar field in D-dimensional de Sitter space - time. By deforming the contour of integration we present it in a form suitable for letting the de Sitter radius tend to infinity, and we demonstrate explicitly for the case D=2 that the quantities ζ(0) and ζ'(0) have the appropriate Minkowski limits. copyright 1997 American Institute of Physics