Counting extensions of imaginary quadratic fields

2021/09/20 by Alexandr Beneš, Beneš, Alexandr
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.09848

openalex publication_date 2021/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal is to obtain an asymptotic formula for the number of quadratic extensions with bounded discriminant of a some quadratic number field with odd class number. This extends an already known result for Q.

Related

• The number of imaginary quadratic fields with prime discriminant and\n class number up to H
• The number of imaginary quadratic fields with a given class number
• Counting multi-quadratic number fields of bounded discriminant
• Class number of real quadratic fields of explicit discriminant
• Class Number Formulas for Certain Biquadratic Fields