Counting integer points in large convex bodies with smooth boundaries containing isolated flat points is oftentimes an intermediate case between balls (or convex bodies with smooth boundaries having everywhere positive curvature) and cubes (or convex polytopes). In this paper, we provide a detailed description of several discrepancy problems in the particular planar case where the boundary coincides locally with the graph of the function ℝ ∋ t -> |t|^γ, with γ > 2. We consider both integer points problems and irregularities of distribution problems. The above “restriction” to a particular family of convex bodies is compensated by the fact that many proofs are elementary. The paper is entirely self-contained.

(2020). Fourier analytic techniques for lattice point discrepancy . Retrieved from http://hdl.handle.net/10446/165595

Fourier analytic techniques for lattice point discrepancy

Brandolini, Luca;
2020-01-01

Abstract

Counting integer points in large convex bodies with smooth boundaries containing isolated flat points is oftentimes an intermediate case between balls (or convex bodies with smooth boundaries having everywhere positive curvature) and cubes (or convex polytopes). In this paper, we provide a detailed description of several discrepancy problems in the particular planar case where the boundary coincides locally with the graph of the function ℝ ∋ t -> |t|^γ, with γ > 2. We consider both integer points problems and irregularities of distribution problems. The above “restriction” to a particular family of convex bodies is compensated by the fact that many proofs are elementary. The paper is entirely self-contained.
2020
Brandolini, Luca; Travaglini, Giancarlo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/165595
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