Explicit Prime Densities for Lucas Sequence Rank Divisibility
Year: 2026
Type: preprint
Abstract: Let $U$ be a Lucas sequence, $p$ be a prime, and $ρ_U(p)$ be the rank of appearance of $p$ in $U$, that is, the least positive integer $n$ such that $p\mid U_n$, if it exists. 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 $d\geq 1$.
Source: arXiv (Cornell University)
Author: Da Conceição, Joaquim Cera
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155352160
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