Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917777121476608 |
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| author | Day, Tori DeLand, Rebecca Juul, Jamie Thomas, Cigole Thompson, Bianca Tobin, Bella |
| author_facet | Day, Tori DeLand, Rebecca Juul, Jamie Thomas, Cigole Thompson, Bianca Tobin, Bella |
| contents | 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 Hamblen-Jones-Madhu regarding the dynamical irreducibility of particular families of unicritical polynomials. We also investigate dynamical irreducibility conditions for cubic and shifted linearized polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields Day, Tori DeLand, Rebecca Juul, Jamie Thomas, Cigole Thompson, Bianca Tobin, Bella Number Theory Dynamical Systems 37P25, 37P05, 11T06 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 Hamblen-Jones-Madhu regarding the dynamical irreducibility of particular families of unicritical polynomials. We also investigate dynamical irreducibility conditions for cubic and shifted linearized polynomials. |
| title | Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields |
| topic | Number Theory Dynamical Systems 37P25, 37P05, 11T06 |
| url | https://arxiv.org/abs/2409.10467 |