Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912255853985792 |
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| author | Brandolini, Luca Colzani, Leonardo Travaglini, Giancarlo |
| author_facet | Brandolini, Luca Colzani, Leonardo Travaglini, Giancarlo |
| contents | W. Schmidt, H. Montgomery, and J. Beck proved a result on irregularities of distribution with respect to $d$-dimensional balls. In this paper, we extend their result to any $d$-dimensional convex body with a smooth boundary and finite order of contact. As an intermediate step, we prove a geometric inequality for the Fourier transform of the characteristic function of a convex body. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies Brandolini, Luca Colzani, Leonardo Travaglini, Giancarlo Number Theory 11K38, 42B10 W. Schmidt, H. Montgomery, and J. Beck proved a result on irregularities of distribution with respect to $d$-dimensional balls. In this paper, we extend their result to any $d$-dimensional convex body with a smooth boundary and finite order of contact. As an intermediate step, we prove a geometric inequality for the Fourier transform of the characteristic function of a convex body. |
| title | Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies |
| topic | Number Theory 11K38, 42B10 |
| url | https://arxiv.org/abs/2503.00973 |