Classification of quadratic forms over finite fields with maximal and minimal Artin-Schreier curves
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912123372699648 |
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| author | Chen, Ruikai |
| author_facet | Chen, Ruikai |
| contents | This paper explores quadratic forms over finite fields with associated Artin-Schreier curves. Specifically, we investigate quadratic forms of $\mathbb F_{q^n}/\mathbb F_q$ represented by polynomials over $\mathbb F_{q^n}$ with $q$ odd, characterizing them using certain matrices defined by coefficients of the polynomials. In particular, a comprehensive treatment will be given for those polynomials whose coefficients all lie in $\mathbb F_q$. Afterwards, the results on quadratic forms will be applied to get maximal and minimal Artin-Schreier curves explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of quadratic forms over finite fields with maximal and minimal Artin-Schreier curves Chen, Ruikai Number Theory This paper explores quadratic forms over finite fields with associated Artin-Schreier curves. Specifically, we investigate quadratic forms of $\mathbb F_{q^n}/\mathbb F_q$ represented by polynomials over $\mathbb F_{q^n}$ with $q$ odd, characterizing them using certain matrices defined by coefficients of the polynomials. In particular, a comprehensive treatment will be given for those polynomials whose coefficients all lie in $\mathbb F_q$. Afterwards, the results on quadratic forms will be applied to get maximal and minimal Artin-Schreier curves explicitly. |
| title | Classification of quadratic forms over finite fields with maximal and minimal Artin-Schreier curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.11705 |