Determinants of the Laplacians on complex projective spaces Pn(C) (n ≥ 1)

In this paper we give explicit formulae for the determinants of the Laplacians on the n-dimensional complex projective spaces Pn(C) (n≥1). This explicit computation of the determinants of the Laplacians ΔPn(C) is appearing for the first time in the Literature. We also discuss in clear terms other spectral invariants on Pn(C) - the Minakshisundaram-Pleijel coefficients and Minakshisundaram-Pleijel zeta functions.