Behaviour of Newton Polygon over polynomial composition
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911115455234048 |
|---|---|
| author | Jakhar, Anuj Laishram, Shanta Srinivas, Kotyada Yadav, Prabhakar |
| author_facet | Jakhar, Anuj Laishram, Shanta Srinivas, Kotyada Yadav, Prabhakar |
| contents | In this paper, we study the structure of Newton polygons for compositions of polynomials over the rationals. We establish sufficient conditions under which the successive vertices of the Newton polygon of the composition $ g(f^n(x)) $ with respect to a prime $ p $ can be explicitly described in terms of the Newton polygon of the polynomial $ g(x) $. Our results provide deeper insights into how the Newton polygon of a polynomial evolves under iteration and composition, with applications to the study of dynamical irreducibility, eventual stability, non-monogenity of tower of number fields, etc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06883 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Behaviour of Newton Polygon over polynomial composition Jakhar, Anuj Laishram, Shanta Srinivas, Kotyada Yadav, Prabhakar Number Theory Dynamical Systems 11R09 (Primary), 11S05, 37P05 (Secondary) In this paper, we study the structure of Newton polygons for compositions of polynomials over the rationals. We establish sufficient conditions under which the successive vertices of the Newton polygon of the composition $ g(f^n(x)) $ with respect to a prime $ p $ can be explicitly described in terms of the Newton polygon of the polynomial $ g(x) $. Our results provide deeper insights into how the Newton polygon of a polynomial evolves under iteration and composition, with applications to the study of dynamical irreducibility, eventual stability, non-monogenity of tower of number fields, etc. |
| title | Behaviour of Newton Polygon over polynomial composition |
| topic | Number Theory Dynamical Systems 11R09 (Primary), 11S05, 37P05 (Secondary) |
| url | https://arxiv.org/abs/2501.06883 |