Asymptotic distribution of CM points on the reduction of the Drinfeld modular curve
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916011184226304 |
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| author | Alvarado, Matias Pérez-Piña, Patricio |
| author_facet | Alvarado, Matias Pérez-Piña, Patricio |
| contents | We study a distribution problem over global function fields. More precisely, we describe the asymptotic distribution of rank $2$ CM Drinfeld modules among the irreducible components of the analytic reduction of the Drinfeld modular curve. Our approach relies on the properties of the building map and the spectral decomposition of the adjacency operator on a quotient of the Bruhat-Tits tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05069 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic distribution of CM points on the reduction of the Drinfeld modular curve Alvarado, Matias Pérez-Piña, Patricio Number Theory 11G09, 11T55, 11R58, 11F25, 11F72 We study a distribution problem over global function fields. More precisely, we describe the asymptotic distribution of rank $2$ CM Drinfeld modules among the irreducible components of the analytic reduction of the Drinfeld modular curve. Our approach relies on the properties of the building map and the spectral decomposition of the adjacency operator on a quotient of the Bruhat-Tits tree. |
| title | Asymptotic distribution of CM points on the reduction of the Drinfeld modular curve |
| topic | Number Theory 11G09, 11T55, 11R58, 11F25, 11F72 |
| url | https://arxiv.org/abs/2604.05069 |