Abstract
The Walfisz-like formula for the number of lattice points of an arbitrary m-dimensional lattice in a hyper-ellipsoid with given semi-axes is derived from Poisson's summation formula. Applications to (i) the evaluation of certain lattice sums and (ii) the calculation of the expressions for the density of states of a single non-relativistic particle as well as of a relativistic particle enclosed in a rectangular m-dimensional box of finite size and subject to different boundary conditions are given.
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