Counting modular forms by rationality field
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913194891542528 |
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| author | Cowan, Alex Martin, Kimball |
| author_facet | Cowan, Alex Martin, Kimball |
| contents | We investigate the distribution of degrees and rationality fields of weight 2 newforms. In particular, we give heuristic upper bounds on how often degree $d$ rationality fields occur for squarefree levels, and predict finiteness if $d \ge 7$. When $d=2$, we make predictions about how frequently specific quadratic fields occur, prove lower bounds, and conjecture that $\mathbb{Q}(\sqrt 5)$ is the most common quadratic rationality field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10357 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting modular forms by rationality field Cowan, Alex Martin, Kimball Number Theory 11F11, 11F30, 11G18, 11Y35 We investigate the distribution of degrees and rationality fields of weight 2 newforms. In particular, we give heuristic upper bounds on how often degree $d$ rationality fields occur for squarefree levels, and predict finiteness if $d \ge 7$. When $d=2$, we make predictions about how frequently specific quadratic fields occur, prove lower bounds, and conjecture that $\mathbb{Q}(\sqrt 5)$ is the most common quadratic rationality field. |
| title | Counting modular forms by rationality field |
| topic | Number Theory 11F11, 11F30, 11G18, 11Y35 |
| url | https://arxiv.org/abs/2301.10357 |