Sums of Reciprocals of Fractional Parts II
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917069817118720 |
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| author | Fregoli, Reynold |
| author_facet | Fregoli, Reynold |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02566 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sums of Reciprocals of Fractional Parts II Fregoli, Reynold Number Theory 11P21, 11H16, 11J13 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. |
| title | Sums of Reciprocals of Fractional Parts II |
| topic | Number Theory 11P21, 11H16, 11J13 |
| url | https://arxiv.org/abs/2304.02566 |