Arithmetic dynamics of a discrete Painlevé equation
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_ | 1866918291315884032 |
|---|---|
| author | Joshi, Nalini Roffelsen, Pieter |
| author_facet | Joshi, Nalini Roffelsen, Pieter |
| contents | We consider the orbits of a discrete Painlevé equation over finite fields and show that the number of points in such orbits satisfy the Hasse bound. The orbits turn out to lie on algebraic curves, whose defining polynomials are given explicitly. Moreover, these curves are shown to have genus less than or equal to one, which contrasts sharply with the case of discrete Painlevé equations over $\mathbb{C}$, whose generic solutions are believed to be more transcendental than elliptic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18578 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arithmetic dynamics of a discrete Painlevé equation Joshi, Nalini Roffelsen, Pieter Exactly Solvable and Integrable Systems Dynamical Systems 11G20, 33E17, 37P05, 39A13 We consider the orbits of a discrete Painlevé equation over finite fields and show that the number of points in such orbits satisfy the Hasse bound. The orbits turn out to lie on algebraic curves, whose defining polynomials are given explicitly. Moreover, these curves are shown to have genus less than or equal to one, which contrasts sharply with the case of discrete Painlevé equations over $\mathbb{C}$, whose generic solutions are believed to be more transcendental than elliptic functions. |
| title | Arithmetic dynamics of a discrete Painlevé equation |
| topic | Exactly Solvable and Integrable Systems Dynamical Systems 11G20, 33E17, 37P05, 39A13 |
| url | https://arxiv.org/abs/2508.18578 |