Positive lower density for prime divisors of generic linear recurrences [article]

Olli Järviniemi
2021 arXiv   pre-print
Let d ≥ 3 be an integer and let P ∈ℤ[x] be a polynomial of degree d whose Galois group is S_d. Let (a_n) be a linearly recuresive sequence of integers which has P as its characteristic polynomial. We prove, under the generalized Riemann hypothesis, that the lower density of the set of primes which divide at least one element of the sequence (a_n) is positive.
arXiv:2102.04042v1 fatcat:oxhm3skwgrgytmtsjss2wmitlu