The Product of linear forms over function fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866912129903230976 |
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| author | Guo, Wenyu Liu, Xuan Shi, Ronggang |
| author_facet | Guo, Wenyu Liu, Xuan Shi, Ronggang |
| contents | The aim of this paper is to study the product of $n$ linear forms over function fields. We calculate the maximum value of the minima of the forms with determinant one when $n$ is small. The value is equal to the natural bound given by algebraic number theory. Our proof is based on a reduction theory of diagonal group orbits on homogeneous spaces. We also show that the forms defined algebraically correspond to periodic orbits with respect to the diagonal group actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Product of linear forms over function fields Guo, Wenyu Liu, Xuan Shi, Ronggang Number Theory Dynamical Systems The aim of this paper is to study the product of $n$ linear forms over function fields. We calculate the maximum value of the minima of the forms with determinant one when $n$ is small. The value is equal to the natural bound given by algebraic number theory. Our proof is based on a reduction theory of diagonal group orbits on homogeneous spaces. We also show that the forms defined algebraically correspond to periodic orbits with respect to the diagonal group actions. |
| title | The Product of linear forms over function fields |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2411.12264 |