Geodesic
Primitive Points in Rational Polygons
Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 850-870

Voir la notice de l'article provenant de la source Cambridge

DOI

Let ${\mathcal{A}}$ be a star-shaped polygon in the plane, with rational vertices, containing the origin. The number of primitive lattice points in the dilate $t{\mathcal{A}}$ is asymptotically $\frac{6}{\unicode[STIX]{x1D70B}^{2}}\text{Area}(t{\mathcal{A}})$ as $t\rightarrow \infty$. We show that the error term is both $\unicode[STIX]{x1D6FA}_{\pm }(t\sqrt{\log \log t})$ and $O(t(\log t)^{2/3}(\log \log t)^{4/3})$. Both bounds extend (to the above class of polygons) known results for the isosceles right triangle, which appear in the literature as bounds for the error term in the summatory function for Euler’s $\unicode[STIX]{x1D719}(n)$.
DOI : 10.4153/S0008439520000090
Mots-clés : Primitive points in polygons, visible points, Euler’s Totient function, Error term, rational polygons 
Bárány, Imre; Martin, Greg; Naslund, Eric; Robins, Sinai. Primitive Points in Rational Polygons. Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 850-870. doi: 10.4153/S0008439520000090
@article{10_4153_S0008439520000090,
     author = {B\'ar\'any, Imre and Martin, Greg and Naslund, Eric and Robins, Sinai},
     title = {Primitive {Points} in {Rational} {Polygons}},
     journal = {Canadian mathematical bulletin},
     pages = {850--870},
     year = {2020},
     volume = {63},
     number = {4},
     doi = {10.4153/S0008439520000090},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000090/}
}
TY  - JOUR
AU  - Bárány, Imre
AU  - Martin, Greg
AU  - Naslund, Eric
AU  - Robins, Sinai
TI  - Primitive Points in Rational Polygons
JO  - Canadian mathematical bulletin
PY  - 2020
SP  - 850
EP  - 870
VL  - 63
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000090/
DO  - 10.4153/S0008439520000090
ID  - 10_4153_S0008439520000090
ER  - 
%0 Journal Article
%A Bárány, Imre
%A Martin, Greg
%A Naslund, Eric
%A Robins, Sinai
%T Primitive Points in Rational Polygons
%J Canadian mathematical bulletin
%D 2020
%P 850-870
%V 63
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000090/
%R 10.4153/S0008439520000090
%F 10_4153_S0008439520000090

Cité par Sources :