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arXiv · 2609.23214

The variance of the number of lattice points in narrow sectors

Stephen Lester·Ezra Waxman·Nadav Yesha
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Abstract

We study the variance of the number of lattice points in smoothed narrow sectors, where the average is taken over the position of the sectors. There are three regimes corresponding to specific ranges for the open angle of the sectors and in each we obtain an asymptotic formula for the variance.

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Stephen Lester, Ezra Waxman, Nadav Yesha. 2026-09-19. The variance of the number of lattice points in narrow sectors. https://arxiv.org/abs/2609.23214

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