Explicit Prime Densities for the Rank of Appearance in Lucas Sequences
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918515522404352 |
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| author | Da Conceição, Joaquim Cera |
| author_facet | Da Conceição, Joaquim Cera |
| contents | Let $U$ be a Lucas sequence, $p$ be prime, and $ρ_U(p)$ be the rank of appearance of $p$ in $U$. We derive closed-form formulas for the Dirichlet density of primes $p$ for which $d\mid ρ_U(p)$, where $d\geq 1$ is a fixed integer. Our results complete the work of Sanna ($2022$) by covering all $U$ and all $d\geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20014 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit Prime Densities for the Rank of Appearance in Lucas Sequences Da Conceição, Joaquim Cera Number Theory 11B39 (Primary) 11R45, 11R18, 11R32 (Secondary) Let $U$ be a Lucas sequence, $p$ be prime, and $ρ_U(p)$ be the rank of appearance of $p$ in $U$. We derive closed-form formulas for the Dirichlet density of primes $p$ for which $d\mid ρ_U(p)$, where $d\geq 1$ is a fixed integer. Our results complete the work of Sanna ($2022$) by covering all $U$ and all $d\geq 1$. |
| title | Explicit Prime Densities for the Rank of Appearance in Lucas Sequences |
| topic | Number Theory 11B39 (Primary) 11R45, 11R18, 11R32 (Secondary) |
| url | https://arxiv.org/abs/2604.20014 |