Functional determinant of Laplacian on Cayley projective plane $${\mathbf {P}}^\mathbf{2 }$$($${\mathbf {Cay}}$$)

Abstract

This paper presents explicit formulae for the determinants of the Laplacians on the Cayley projective plane $$\mathbf {P}^{2}({\mathrm{Cay}})$$ . The explicit calculation of this spectral invariant associated with $$\mathbf {P}^{2}({\mathrm{Cay}})$$ is appearing for the first time in the literature. Other spectral invariants on $$\mathbf {P}^{2}({\mathrm{Cay}})$$ – the Minakshisundaram–Pleijel coefficients and Minakshisundaram–Pleijel zeta functions are also explicitly discussed.