Lattice Points in Thin Sectors

par Ezra Waxman (University of Haifa, Israël)

lundi 7 oct. 2024, 15:30 → 16:30 Europe/Paris

Salle Grisvard, IHP, Paris

On the circle of radius $R$ centred at the origin, consider a "thin" sector about the fixed line $y =\alpha x$ with edges given by the lines $y = (\alpha \pm \epsilon) x$, where $\epsilon = \epsilon_R \rightarrow 0$ as $R \to \infty$. We discuss an asymptotic count for $S_{\alpha}(\epsilon,R)$, the number of integer lattice points lying in such a sector, and moreover present results concerning the variance of such lattice points across sectors.