Secondary terms in the counting functions of quartic fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911101808017408 |
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| author | Shankar, Arul Tsimerman, Jacob |
| author_facet | Shankar, Arul Tsimerman, Jacob |
| contents | We prove that the smoothed counting function of the set of quartic fields, satisfying any finite set of local conditions, can be written as a linear combination of $X,X^{5/6}\log X,X^{5/6}$, upto an error term of $O(X^{13/16+o(1)})$. For certain sets of local conditions, namely, those cutting out ``$S_4$-families'' of quartic fields, we explicitly determine the leading constants of the secondary terms. We moreover express these constants in terms of secondary mass formulas associated to families of quartic fields |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Secondary terms in the counting functions of quartic fields Shankar, Arul Tsimerman, Jacob Number Theory We prove that the smoothed counting function of the set of quartic fields, satisfying any finite set of local conditions, can be written as a linear combination of $X,X^{5/6}\log X,X^{5/6}$, upto an error term of $O(X^{13/16+o(1)})$. For certain sets of local conditions, namely, those cutting out ``$S_4$-families'' of quartic fields, we explicitly determine the leading constants of the secondary terms. We moreover express these constants in terms of secondary mass formulas associated to families of quartic fields |
| title | Secondary terms in the counting functions of quartic fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.02381 |