Sparsity of stable primes for dynamical sequences
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912087284908032 |
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| author | König, Joachim |
| author_facet | König, Joachim |
| contents | We show that a dynamical sequence $(f_n)_{n\in \mathbb{N}}$ of polynomials over a number field whose set of stable primes is of positive density must necessarily have a very restricted, and in particular ``near-solvable" dynamical Galois group. Together with existing heuristics, our results suggest moreover that a polynomial $f$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparsity of stable primes for dynamical sequences König, Joachim Number Theory Dynamical Systems Group Theory We show that a dynamical sequence $(f_n)_{n\in \mathbb{N}}$ of polynomials over a number field whose set of stable primes is of positive density must necessarily have a very restricted, and in particular ``near-solvable" dynamical Galois group. Together with existing heuristics, our results suggest moreover that a polynomial $f$ 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. |
| title | Sparsity of stable primes for dynamical sequences |
| topic | Number Theory Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2402.18772 |