TY - JOUR

T1 - Geometry of the Gauss map and lattice points in convex domains

AU - Brandolini, L.

AU - Colzani, L.

AU - Iosevich, A.

AU - Podkorytov, A.

AU - Travaglini, G.

N1 - Funding Information: Acknowledgement. This research was supported in part by NSF grant DMS97-06825, INdAM, Integration Program No. 326.53 and RFFI No. 00-15-96-022.

PY - 2001

Y1 - 2001

N2 - Let Ω be a convex planar domain, with no curvature or regularity assumption on the boundary. Let Nθ(R) = card{RΩθ∩ℤ2}, where Ωθ denotes the rotation of Ω by θ. It is proved that, up to a small logarithmic transgression, Nθ(R) = |Ω\R2 + O(R2/3), for almost every rotation. A refined result based on the fractal structure of the image of the boundary of Ω under the Gauss map is also obtained.

AB - Let Ω be a convex planar domain, with no curvature or regularity assumption on the boundary. Let Nθ(R) = card{RΩθ∩ℤ2}, where Ωθ denotes the rotation of Ω by θ. It is proved that, up to a small logarithmic transgression, Nθ(R) = |Ω\R2 + O(R2/3), for almost every rotation. A refined result based on the fractal structure of the image of the boundary of Ω under the Gauss map is also obtained.

UR - http://www.scopus.com/inward/record.url?scp=25444445286&partnerID=8YFLogxK

U2 - 10.1112/S0025579300014376

DO - 10.1112/S0025579300014376

M3 - Article

AN - SCOPUS:25444445286

VL - 48

SP - 107

EP - 117

JO - Mathematika

JF - Mathematika

SN - 0025-5793

IS - 1-2

ER -