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Geometry of the Gauss map and lattice points in convex domains. / Brandolini, L.; Colzani, L.; Iosevich, A.; Podkorytov, A.; Travaglini, G.

In: Mathematika, Vol. 48, No. 1-2, 2001, p. 107-117.

Research output: Contribution to journal › Article › peer-review

Harvard

Brandolini, L, Colzani, L, Iosevich, A, Podkorytov, A & Travaglini, G 2001, 'Geometry of the Gauss map and lattice points in convex domains', Mathematika, vol. 48, no. 1-2, pp. 107-117. https://doi.org/10.1112/S0025579300014376

APA

Brandolini, L., Colzani, L., Iosevich, A., Podkorytov, A., & Travaglini, G. (2001). Geometry of the Gauss map and lattice points in convex domains. Mathematika, 48(1-2), 107-117. https://doi.org/10.1112/S0025579300014376

Vancouver

Brandolini L, Colzani L, Iosevich A, Podkorytov A, Travaglini G. Geometry of the Gauss map and lattice points in convex domains. Mathematika. 2001;48(1-2):107-117. https://doi.org/10.1112/S0025579300014376

Author

Brandolini, L. ; Colzani, L. ; Iosevich, A. ; Podkorytov, A. ; Travaglini, G. / Geometry of the Gauss map and lattice points in convex domains. In: Mathematika. 2001 ; Vol. 48, No. 1-2. pp. 107-117.

BibTeX

@article{b7d0a4455b18490e9d32d0cf7c9f348b,
title = "Geometry of the Gauss map and lattice points in convex domains",
abstract = "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.",
author = "L. Brandolini and L. Colzani and A. Iosevich and A. Podkorytov and G. Travaglini",
note = "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.",
year = "2001",
doi = "10.1112/S0025579300014376",
language = "English",
volume = "48",
pages = "107--117",
journal = "Mathematika",
issn = "0025-5793",
publisher = "Cambridge University Press",
number = "1-2",

}

RIS

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 -

ID: 86292039