Polynomial compositions with large monodromy groups and applications to arithmetic dynamics
J König, D Neftin, S Rosenberg - arXiv preprint arXiv:2401.17872, 2024 - arxiv.org
For a composition $ f= f_1\circ\cdots\circ f_r $ of polynomials $ f_i\in\mathbb Q [x] $ of
degrees $ d_i\geq 5$ with alternating or symmetric monodromy group, we show that the …
degrees $ d_i\geq 5$ with alternating or symmetric monodromy group, we show that the …
Sparsity of stable primes for dynamical sequences
J König - Bulletin of the London Mathematical Society, 2024 - Wiley Online Library
We show that a dynamical sequence (fn) n∈ N (f_n)_n∈N of polynomials over a number
field whose set of stable primes is of positive density must necessarily have a very restricted …
field whose set of stable primes is of positive density must necessarily have a very restricted …
On the frequency of primes preserving dynamical irreducibility of polynomials
A Ostafe, IE Shparlinski - arXiv preprint arXiv:2407.20464, 2024 - arxiv.org
Towards a well-known open question in arithmetic dynamics, L. M\'erai, A. Ostafe and IE
Shparlinski (2023), have shown, for a class of polynomials $ f\in\mathbb Z [X] $, which in …
Shparlinski (2023), have shown, for a class of polynomials $ f\in\mathbb Z [X] $, which in …
Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields
T Day, R DeLand, J Juul, C Thomas… - arXiv preprint arXiv …, 2024 - arxiv.org
We determine necessary and sufficient conditions for unicritical polynomials to be
dynamically irreducible over finite fields. This result extends the results of Boston-Jones and …
dynamically irreducible over finite fields. This result extends the results of Boston-Jones and …
On the set of stable primes for postcritically infinite maps over number fields
J König - arXiv preprint arXiv:2408.13477, 2024 - arxiv.org
Many interesting questions in arithmetic dynamics revolve, in one way or another, around
the (local and/or global) reducibility behavior of iterates of a polynomial. We show that for …
the (local and/or global) reducibility behavior of iterates of a polynomial. We show that for …
On the inverse stability of
YGQ Ji - arXiv preprint arXiv:2501.07409, 2025 - arxiv.org
Let $ K $ be a field and $\phi (z)\in K [z] $ be a polynomial. Define $\Phi (z):=\frac {1}{\phi
(z)}\in K (z). $ For $ n\in\mathbb {N}^* $, let the $ n $-th iterate of $\Phi (z) $ be defined as …
(z)}\in K (z). $ For $ n\in\mathbb {N}^* $, let the $ n $-th iterate of $\Phi (z) $ be defined as …