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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.16729 |
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| _version_ | 1866913134558576640 |
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| author | Ito, Tetsushi Takeuchi, Daichi Tsushima, Takahiro |
| author_facet | Ito, Tetsushi Takeuchi, Daichi Tsushima, Takahiro |
| contents | In our previous work, we gave a formula for the Frobenius eigenvalues of van der Geer--van der Vlugt curves in characteristic 2 by considering suitable quotients of the curve. Although the formula is explicit, it depends on many choices, which makes the formula complicated. In this article, we take a different approach using a factorization of additive polynomials, and prove a new formula. The resulting formula is simpler and is useful for explicit computations. As applications, we provide a method for constructing maximal and minimal van der Geer--van der Vlugt curves, and show that every such curve arises from this construction. We also compute various examples of van der Geer--van der Vlugt curves and study their periods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16729 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Factorization of Additive Polynomials and van der Geer--van der Vlugt curves in characteristic 2 Ito, Tetsushi Takeuchi, Daichi Tsushima, Takahiro Number Theory In our previous work, we gave a formula for the Frobenius eigenvalues of van der Geer--van der Vlugt curves in characteristic 2 by considering suitable quotients of the curve. Although the formula is explicit, it depends on many choices, which makes the formula complicated. In this article, we take a different approach using a factorization of additive polynomials, and prove a new formula. The resulting formula is simpler and is useful for explicit computations. As applications, we provide a method for constructing maximal and minimal van der Geer--van der Vlugt curves, and show that every such curve arises from this construction. We also compute various examples of van der Geer--van der Vlugt curves and study their periods. |
| title | Factorization of Additive Polynomials and van der Geer--van der Vlugt curves in characteristic 2 |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.16729 |