Reynold Fregoli
Published 2023-04-05Version 1
In this paper we generalise a result of Kruse (1964) concerning the almost sure order of magnitude of sums of reciprocals of fractional parts, thereby solving a conjecture posed by Beresnevich, Haynes, and Velani. The methods are based both on the geometry of numbers and probability theory.
Comments: - Appendix by Michael Bj\"orklund, Reynold Fregoli, and Alexander Gorodnik - This is the NEW VERSION of a paper entitled Sums of Reciprocals of Fractional Parts over Aligned Boxes (identifier arXiv:2101.11094) by the same author. The previous version will not be published
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