Monnet, Sebastian;
(2025)
Counting wild quartics with prescribed
discriminant and Galois closure group.
Journal of Number Theory
, 269
pp. 157-202.
10.1016/j.jnt.2024.10.008.
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Abstract
Given a 2-adic field K, we give a formula 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 refinements of Serre’s mass formula, which will have applications to the arithmetic statistics of number fields.
| Type: | Article |
|---|---|
| Title: | Counting wild quartics with prescribed discriminant and Galois closure group |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jnt.2024.10.008 |
| Publisher version: | https://doi.org/10.1016/j.jnt.2024.10.008 |
| Language: | English |
| Additional information: | Copyright © 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Arithmetic statistics; Local fields; p-Adic fields; Serre’s mass formula; Counting number fields |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10200144 |
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