Regularized determinant of the Laplacian on forms over odd dimensional projective spaces

Abstract

We establish formulae for the regularized determinant of the twisted Laplacians
on forms over odd dimensional real projective spaces. This work corresponds to
a generalization of the previous formula for this type of space and we prove the
equivalence in the common cases, what leads to interesting, if simple, identities
involving special values of Bernoulli polynomials and the Riemann zeta function.
As application, we calculate the Analytic Torsion of these spaces in relation to all
unitary representations of their fundamental group.