A REMARK ON THE ASYMPTOTIC PROPERTIES OF EIGENVALUES AND THE LATTICE POINT PROBLEM

Abstract

The asymptotic distribution of eigenvalues of elliptic self-adjoint operators on the flat torus is discussed. A relation between a geometrical property of the operators and the error terms in the distribution formulas is given in the case when the operators have constant coefficients. As a corollary, the error terms can be determined only by the order of the operators and the dimension of the torus. This result also gives an information on the number of lattice points inside convex or nonconvex bodies in Rⁿ.