A1 Refereed original research article in a scientific journal
Positive lower density for prime divisors of generic linear recurrences
Authors: Järviniemi Olli
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2023
Journal: Mathematical Proceedings of the Cambridge Philosophical Society
Journal name in source: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Journal acronym: MATH PROC CAMBRIDGE
Number of pages: 12
ISSN: 0305-0041
eISSN: 1469-8064
DOI: https://doi.org/10.1017/S0305004123000257
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1017/S0305004123000257
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/179731581
Self-archived copy's licence: CC BY SA
Self-archived copy's version: Publisher`s PDF
Let d = 3 be an integer and let P ? Z[x] be a polynomial of degree d whose Galois group is Sd. Let (a(n)) be a non-degenerate linearly recursive sequence of integers which has P as its characteristic polynomial. We prove, under the generalised Riemann hypothesis, that the lower density of the set of primes which divide at least one non-zero element of the sequence (a(n)) is positive.
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