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 $y=(\alpha \pm ϵ)x$, where $ϵ={ϵ}_R\to 0$ as $R\to \mathrm{\infty }$. We discuss an asymptotic count for $S_{\alpha }(ϵ,R)$, the number of integer lattice points lying in such a sector, and moreover present results concerning the variance of such lattice points across sectors.