1 results
Primitive Points in Rational Polygons
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 4 / December 2020
- Published online by Cambridge University Press:
- 30 January 2020, pp. 850-870
- Print publication:
- December 2020
-
- Article
- Export citation
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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 
$\unicode[STIX]{x1D719}(n)$.
