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

2023/04/06 by Sebastian Monnet, Monnet, Sebastian
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2304.03154

openalex publication_date 2023/04/06 · openalex created_date 2023/04/09 · openalex updated_date 2026/07/28

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.

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