Counting Drinfeld modules with prescribed local conditions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916499810156544 |
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| author | Phillips, Tristan |
| author_facet | Phillips, Tristan |
| contents | We give asymptotics for the number of Drinfeld $\mathbb{F}_q[T]$-modules over $\mathbb{F}_q(T)$ of a given height, which satisfy prescribed sets of local conditions. This is done by relating our problem to a problem about counting points on weighted projective spaces. Our results for counting points of bounded height on weighted projective spaces over global function fields may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05576 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Counting Drinfeld modules with prescribed local conditions Phillips, Tristan Number Theory Algebraic Geometry Primary 11G09, Secondary 11G18, 11G50, 11D45, 14G05 We give asymptotics for the number of Drinfeld $\mathbb{F}_q[T]$-modules over $\mathbb{F}_q(T)$ of a given height, which satisfy prescribed sets of local conditions. This is done by relating our problem to a problem about counting points on weighted projective spaces. Our results for counting points of bounded height on weighted projective spaces over global function fields may be of independent interest. |
| title | Counting Drinfeld modules with prescribed local conditions |
| topic | Number Theory Algebraic Geometry Primary 11G09, Secondary 11G18, 11G50, 11D45, 14G05 |
| url | https://arxiv.org/abs/2209.05576 |