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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2506.15274 |
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| _version_ | 1866912437862662144 |
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| author | Bera, Tanmoy Malavika, E. |
| author_facet | Bera, Tanmoy Malavika, E. |
| contents | In this article we prove that if the additive energy of a strictly increasing sequence $(a_n)$ of natural numbers is less than $N^3/(\log N)^C$ for some $C\geq13.155$, then $(\{a_nα\})$ has Poissonian pair correlation for almost all $α\in\mathbb{R}.$ This provides a lower bound for the exponent $C$ in the additive energy bound established by Bloom and Walker[3]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metric Poissonian pair correlationa and additive energy Bera, Tanmoy Malavika, E. Number Theory 11K06 In this article we prove that if the additive energy of a strictly increasing sequence $(a_n)$ of natural numbers is less than $N^3/(\log N)^C$ for some $C\geq13.155$, then $(\{a_nα\})$ has Poissonian pair correlation for almost all $α\in\mathbb{R}.$ This provides a lower bound for the exponent $C$ in the additive energy bound established by Bloom and Walker[3]. |
| title | Metric Poissonian pair correlationa and additive energy |
| topic | Number Theory 11K06 |
| url | https://arxiv.org/abs/2506.15274 |