Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913201447239680 |
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| author | Monnet, Sebastian |
| author_facet | Monnet, Sebastian |
| contents | Given a $2$-adic field $K$, we give formulae for the number of totally ramified quartic field extensions $L/K$ with a given discriminant valuation and Galois closure group. We use these formulae to prove a refinement of Serre's mass formula, which will have applications to the arithmetic statistics of number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03154 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group Monnet, Sebastian Number Theory Given a $2$-adic field $K$, we give formulae for the number of totally ramified quartic field extensions $L/K$ with a given discriminant valuation and Galois closure group. We use these formulae to prove a refinement of Serre's mass formula, which will have applications to the arithmetic statistics of number fields. |
| title | Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group |
| topic | Number Theory |
| url | https://arxiv.org/abs/2304.03154 |