On the Dynamical System Generated by the Möbius Transformation at Smooth Times
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916846283784192 |
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| author | Mérai, László Shparlinski, Igor E. |
| author_facet | Mérai, László Shparlinski, Igor E. |
| contents | We study the distribution of the sequence of the first $N$ elements of the discrete dynamical system generated by the Möbius transformation $x \mapsto (αx + β)/(γx + δ)$ over a finite field of $p$ elements at the moments of time that correspond to $Q$-smooth numbers, that is, to numbers composed out of primes up to $Q$. In particular, we obtain nontrivial estimates of exponential sums with such sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Dynamical System Generated by the Möbius Transformation at Smooth Times Mérai, László Shparlinski, Igor E. Number Theory We study the distribution of the sequence of the first $N$ elements of the discrete dynamical system generated by the Möbius transformation $x \mapsto (αx + β)/(γx + δ)$ over a finite field of $p$ elements at the moments of time that correspond to $Q$-smooth numbers, that is, to numbers composed out of primes up to $Q$. In particular, we obtain nontrivial estimates of exponential sums with such sequences. |
| title | On the Dynamical System Generated by the Möbius Transformation at Smooth Times |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.12160 |