Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group

Sebastian Monnet

Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group

Number Theory 2024-01-23 v2

Authors: Sebastian Monnet

Abstract

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.

Keywords

quartic extensions discriminant valuation galois closure group serre mass formula arithmetic statistics 2-adic fields

Cite

@article{arxiv.2304.03154,
  title  = {Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group},
  author = {Sebastian Monnet},
  journal= {arXiv preprint arXiv:2304.03154},
  year   = {2024}
}

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