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Positive lower density for prime divisors of generic linear recurrences.
- Source :
-
Mathematical Proceedings of the Cambridge Philosophical Society . Nov2023, Vol. 175 Issue 3, p467-478. 12p. - Publication Year :
- 2023
-
Abstract
- Let $d \ge 3$ be an integer and let $P \in \mathbb{Z}[x]$ be a polynomial of degree d whose Galois group is $S_d$. 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DENSITY
*INTEGERS
*POLYNOMIALS
*RECURSIVE sequences (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 03050041
- Volume :
- 175
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publication Type :
- Academic Journal
- Accession number :
- 172989924
- Full Text :
- https://doi.org/10.1017/S0305004123000257