Minimal value set binomials and Frobenius nonclassical curves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918129116905472 |
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| author | Aprigio, Tiago Guardieiro, João Paulo |
| author_facet | Aprigio, Tiago Guardieiro, João Paulo |
| contents | In this paper, we characterize all minimal value set binomials over $\mathbb{F}_q$, that is, binomials whose size of the set of images is the smallest possible. With this information, we also classify all quadrinomial curves with separated variables that are $\mathbb{F}_q$-Frobenius nonclassical for the morphism of lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal value set binomials and Frobenius nonclassical curves Aprigio, Tiago Guardieiro, João Paulo Number Theory Algebraic Geometry 14H45, 11C08 (Primary) 14Hxx (Secondary) In this paper, we characterize all minimal value set binomials over $\mathbb{F}_q$, that is, binomials whose size of the set of images is the smallest possible. With this information, we also classify all quadrinomial curves with separated variables that are $\mathbb{F}_q$-Frobenius nonclassical for the morphism of lines. |
| title | Minimal value set binomials and Frobenius nonclassical curves |
| topic | Number Theory Algebraic Geometry 14H45, 11C08 (Primary) 14Hxx (Secondary) |
| url | https://arxiv.org/abs/2508.16541 |