Spectral Invariants of Laplacians on Quaternionic Projective Spaces P n (H) (n ≥ 1

Abstract

This paper presents explicit closed-form formulae for the determinants of the Laplacians on n-dimensional quaternionic projective spaces Pⁿ (H) (n ≥ 1). The explicit calculation of this spectral invariant associated with Pⁿ (H) is novel in the context of spectral theory of the Laplacian on Riemannian manifolds. Other spectral properties of the Laplacian on Pⁿ (H) – the Minakshisundaram-Pleijel coefficients and Minakshisundaram-Pleijel zeta functions are also explicitly discussed.