Random exponential sums and lattice points in regions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929586708676608 |
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| author | Temur, Faruk Sahillioğulları, Cihan |
| author_facet | Temur, Faruk Sahillioğulları, Cihan |
| contents | In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, and $L^{2n}(\mathbb{T}), \ n\in \mathbb{N}$ norms of exponential sums, which can also be interpreted as solutions of diophantine equations or lattice points on surfaces. We establish connections to the well known problems on lattice points in regions such as the Dirichlet divisor problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random exponential sums and lattice points in regions Temur, Faruk Sahillioğulları, Cihan Classical Analysis and ODEs Number Theory Primary: 42A05, 42A61, 42A70, 11P05, 11P21, Secondary: 60G10, 60G50, 60G51 In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, and $L^{2n}(\mathbb{T}), \ n\in \mathbb{N}$ norms of exponential sums, which can also be interpreted as solutions of diophantine equations or lattice points on surfaces. We establish connections to the well known problems on lattice points in regions such as the Dirichlet divisor problem. |
| title | Random exponential sums and lattice points in regions |
| topic | Classical Analysis and ODEs Number Theory Primary: 42A05, 42A61, 42A70, 11P05, 11P21, Secondary: 60G10, 60G50, 60G51 |
| url | https://arxiv.org/abs/2411.06517 |