Angular distribution towards the points of the neighbor-flips modular curve seen by a fast moving observer
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913778791088128 |
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| author | Anderson, Jack Boca, Florin P. Cobeli, Cristian Zaharescu, Alexandru |
| author_facet | Anderson, Jack Boca, Florin P. Cobeli, Cristian Zaharescu, Alexandru |
| contents | Let $h$ be a fixed non-zero integer. For every $t\in \mathbb{R}_+$ and every prime $p$, consider the angles between rays from an observer located at the point $(-tJ_p^2,0)$ on the real axis towards the set of all integral solutions $(x,y)$ of the equation $y^{-1}-x^{-1}\equiv h \pmod{p}$ in the square $[-J_p,J_p]^2$, where $J_p=(p-1)/2$. We prove the existence of the limiting gap distribution for this set of angles as $p\rightarrow \infty$, providing explicit formulas for the corresponding density function, which turns out to be independent of $h$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14993 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Angular distribution towards the points of the neighbor-flips modular curve seen by a fast moving observer Anderson, Jack Boca, Florin P. Cobeli, Cristian Zaharescu, Alexandru Number Theory 11P21 (primary) 11B05, 11L07 (secondary) Let $h$ be a fixed non-zero integer. For every $t\in \mathbb{R}_+$ and every prime $p$, consider the angles between rays from an observer located at the point $(-tJ_p^2,0)$ on the real axis towards the set of all integral solutions $(x,y)$ of the equation $y^{-1}-x^{-1}\equiv h \pmod{p}$ in the square $[-J_p,J_p]^2$, where $J_p=(p-1)/2$. We prove the existence of the limiting gap distribution for this set of angles as $p\rightarrow \infty$, providing explicit formulas for the corresponding density function, which turns out to be independent of $h$. |
| title | Angular distribution towards the points of the neighbor-flips modular curve seen by a fast moving observer |
| topic | Number Theory 11P21 (primary) 11B05, 11L07 (secondary) |
| url | https://arxiv.org/abs/2312.14993 |