Work

Sparsity of stable primes for dynamical sequences

Year: 2024

Type: article

Abstract: We show that a dynamical sequence of polynomials over a number field whose set of stable primes is of positive density must necessarily have a very restricted, and, in particular, virtually prosolvable dynamical Galois group. Together with existing heuristics, our results suggest, moreover, that a polynomial all of whose iterates are irreducible modulo a positive density subset of the primes must necessarily be a composition of linear functions, monomials, and Dickson polynomials.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.13191

Author: Joachim König

Institution: Korea National University of Education

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funders: National Research Foundation, National Research Foundation of Korea