Let Omega be a convex planar domain, with no curvature or regularity assumption on the boundary. Let N-theta (R) = card{ROmega(theta)boolean ANDZ(2)}, where Omega(theta) denotes the rotation of Omega by theta. It is proved that, up to a small logarithmic transgression, N-theta (R) = OmegaR-2 + O(R-2/3), for almost every rotation. A refined result based on the fractal structure of the image of the boundary of Omega under the Gauss map is also obtained

Brandolini, L., Colzani, L., Iosevich, A., Podkorytov, A., Travaglini, G. (2001). Geometry of the Gauss map and lattice points in convex domains. MATHEMATIKA, 48(95-96), 107-117 [10.1112/S0025579300014376].

Geometry of the Gauss map and lattice points in convex domains

Colzani, L;Travaglini, G
2001

Abstract

Let Omega be a convex planar domain, with no curvature or regularity assumption on the boundary. Let N-theta (R) = card{ROmega(theta)boolean ANDZ(2)}, where Omega(theta) denotes the rotation of Omega by theta. It is proved that, up to a small logarithmic transgression, N-theta (R) = OmegaR-2 + O(R-2/3), for almost every rotation. A refined result based on the fractal structure of the image of the boundary of Omega under the Gauss map is also obtained
Articolo in rivista - Articolo scientifico
Lattice points
English
2001
48
95-96
107
117
none
Brandolini, L., Colzani, L., Iosevich, A., Podkorytov, A., Travaglini, G. (2001). Geometry of the Gauss map and lattice points in convex domains. MATHEMATIKA, 48(95-96), 107-117 [10.1112/S0025579300014376].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/5569
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