Lower order terms in the shape of cubic fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912025677922304 |
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| author | Hough, Robert Lee, Eun Hye |
| author_facet | Hough, Robert Lee, Eun Hye |
| contents | We demonstrate equidistribution of the lattice shape of cubic fields when ordered by discriminant, giving an estimate in the Eisenstein series spectrum with a lower order main term. The analysis gives a separate discussion of the contributions of reducible and irreducible binary cubic forms, following a method of Shintani. Our work answers a question posed at the American Institute of Math by giving a precise geometric and spectral description of an evident barrier to equidistribution in the lattice shape. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lower order terms in the shape of cubic fields Hough, Robert Lee, Eun Hye Number Theory We demonstrate equidistribution of the lattice shape of cubic fields when ordered by discriminant, giving an estimate in the Eisenstein series spectrum with a lower order main term. The analysis gives a separate discussion of the contributions of reducible and irreducible binary cubic forms, following a method of Shintani. Our work answers a question posed at the American Institute of Math by giving a precise geometric and spectral description of an evident barrier to equidistribution in the lattice shape. |
| title | Lower order terms in the shape of cubic fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.08417 |