A spectral analogue of the Meinardus theorem on asymptotics of the number of partitions

Abstract

An asymptotic formula for the number of states of Boson gas whose Hamiltonian is given by a positive elliptic pseudo-differential operator of order one on a compact manifold is given under a integrality assumption on the spectrum of the Hamiltonian. This is regarded as an analogue of the Meinardus theorem on asymptotics of the number of partitions of a positive integer.Comment: Introduction has rewritten. In particular, the assumption in the main theorem has been changed. The assumption of main theorem in the old version is not suitable. Some mistakes are fixed. To appear in the journal Asymptotic Analysi