Primitive Points in Rational Polygons

被引：1

作者：

Barany, Imre ^{[1
]}

Martin, Greg ^{[2
]}

Naslund, Eric ^{[3
]}

Robins, Sinai ^{[4
]}

机构：

[1] Hungarian Acad Sci, Renyi Inst Math, Pf 127, H-1364 Budapest, Hungary

[2] UCL, Dept Math, London WC1E 6BT, England

[3] Univ British Columbia, Dept Math, Room 121,1984 Math Rd, Vancouver, BC V6T 1Z2, Canada

[4] Univ Sao Paulo, Inst Math & Estat, BR-05508090 Sao Paulo, Brazil

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2020年 / 63卷 / 04期

基金：

加拿大自然科学与工程研究理事会; 欧洲研究理事会;

关键词：

Primitive points in polygons; visible points; Euler's Totient function; Error term; rational polygons;

D O I：

10.4153/S0008439520000090

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a star-shaped polygon in the plane, with rational vertices, containing the origin. he number of primitive lattice points in the dilate tA is asymptotically 6/pi(2) Area(tA) as t -> infinity. We show that the error term is both Omega(+/-)( t root 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 phi(n).

引用

页码：850 / 870

页数：21

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