Cyclotomic function fields over finite fields with irreducible quadratic modulus
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909129181757440 |
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| author | Arakelian, Nazar Quoos, Luciane |
| author_facet | Arakelian, Nazar Quoos, Luciane |
| contents | Let $\mathbb{F}_q$ be the finite field of order $q$ and $F=\mathbb{F}_q(x)$ the rational function field. In this paper, we give a characterization of the cyclotomic function fields $F(Λ_M)$ with modulus $M$, where $M \in \mathbb{F}_q[T]$ is a monic and irreducible polynomial of degree two. We also provide the full automorphism group of $F(Λ_M)$ in odd characteristic, extending results of \cite{MXY2016} where the automorphism group of $F(Λ_M)$ over $\mathbb{F}_q$ was computed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05424 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cyclotomic function fields over finite fields with irreducible quadratic modulus Arakelian, Nazar Quoos, Luciane Number Theory Algebraic Geometry Let $\mathbb{F}_q$ be the finite field of order $q$ and $F=\mathbb{F}_q(x)$ the rational function field. In this paper, we give a characterization of the cyclotomic function fields $F(Λ_M)$ with modulus $M$, where $M \in \mathbb{F}_q[T]$ is a monic and irreducible polynomial of degree two. We also provide the full automorphism group of $F(Λ_M)$ in odd characteristic, extending results of \cite{MXY2016} where the automorphism group of $F(Λ_M)$ over $\mathbb{F}_q$ was computed. |
| title | Cyclotomic function fields over finite fields with irreducible quadratic modulus |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2309.05424 |