Determinants and Cheeger-Müller Theorem on even dimensional projective spaces

We establish formulae for the regularized determinant of the Laplacian and twisted Laplacian on forms over even dimensional real projective spaces and use them to explicitly calculate the analytic torsion of these spaces with orthogonal and unitary representations of their fundamental group, obtaining the first example to show that this torsion is non-trivial for cyclic complexes associated to even dimensional non-orientable manifolds. Moreover, as discussed in the introduction, the several proofs of the Cheeger-Müller Theorem given throughout years left one specific question unanswered and we answer this question for this type of space.