Sums of Reciprocals of Fractional Parts II

Reynold Fregoli

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arXiv · 2304.02566

Sums of Reciprocals of Fractional Parts II

Reynold Fregoli

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Abstract

We prove an estimate for the number of lattice points lying in certain non-convex Euclidean domains of interest in Diophantine approximation. As an application, we generalise a result of Kruse (1964) concerning the almost sure order of magnitude of sums of reciprocals of fractional parts and solve a conjecture posed by Beresnevich, Haynes, and Velani. The methods are based both on the geometry of numbers and on probability theory.

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Reynold Fregoli. 2023-04-05. Sums of Reciprocals of Fractional Parts II. https://arxiv.org/abs/2304.02566

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