Lattice points in multidimensional bodies

Abstract

Asymptotic expansions for the number of lattice points in regions of the ddimensional Euclidean space are obtained. We assume that the regions are level sets of poly

Lattice points in bodies with algebraic boundary

“…There are several ways to obtain it. We use the following expansion of a sufficiently smooth complex-valued function g : R s → C due to Bentkus and Götze [1]. Let J ∈ N, and x, u 1 , .…”

“…With this choice t lies on the boundary of M ∆(t) (1,1). Hence t ∈ m ∆(t) and the definition (10) or (9) implies, for every…”

“…(1) One only has to observe that A F (R + ε) = A F (R) for R ∈ N and 0 < ε < 1, but vol(D F (R + ε)) − vol(D F (R)) R s/d−1 . Our aim is to give a sharp upper bound for P F (R).…”

“…Recently, Bentkus and Götze [1] studied P F (R) for polynomials F with real coefficients and leading homogeneous part…”