Imaginary mass lens space determinants

Abstract

Functional determinants for a single scalar field with negative mass squared are evaluated on homogeneous lens spaces. For example, on even order spaces, the Hartle--Hawking wave function oscillates about its zeros with increasing amplitude as the (imaginary) mass increases. I also present results for the binary tetrahedral, octahedral and icosahedral factors of the three--sphere. The final answer is given as a quadrature and some graphs are drawn. In the technical evaluation of the infinite sums, the explicit form of the degeneracies is not needed.