Effective equidistribution of Galois orbits for mildly regular test functions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914368282689536 |
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| author | Carneiro, Emanuel Das, Mithun Kumar |
| author_facet | Carneiro, Emanuel Das, Mithun Kumar |
| contents | In this paper we provide a detailed study on effective versions of the celebrated Bilu's equidistribution theorem for Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus, identifying the quantitative dependence of the convergence in terms of the regularity of the test functions considered. We develop a general Fourier analysis framework that extends previous results obtained by Petsche (2005), and by D'Andrea, Narváez-Clauss and Sombra (2017). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16294 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective equidistribution of Galois orbits for mildly regular test functions Carneiro, Emanuel Das, Mithun Kumar Number Theory Classical Analysis and ODEs 11G50, 11K38, 43A25 In this paper we provide a detailed study on effective versions of the celebrated Bilu's equidistribution theorem for Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus, identifying the quantitative dependence of the convergence in terms of the regularity of the test functions considered. We develop a general Fourier analysis framework that extends previous results obtained by Petsche (2005), and by D'Andrea, Narváez-Clauss and Sombra (2017). |
| title | Effective equidistribution of Galois orbits for mildly regular test functions |
| topic | Number Theory Classical Analysis and ODEs 11G50, 11K38, 43A25 |
| url | https://arxiv.org/abs/2411.16294 |