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Rencontres de théorie analytique des nombres
# Lattice Points in Thin Sectors

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Salle Grisvard, IHP, Paris
### Salle Grisvard, IHP, Paris

Description

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.

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Régis de la Bretèche

Cathy Swaenepoel

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