Counting multi-quadratic number fields of bounded discriminant

TL;DR

This paper establishes an asymptotic count for multi-quadratic number fields with bounded discriminant, providing explicit formulas and extending results to totally real fields, with improved error estimates.

Contribution

It introduces a precise asymptotic formula for counting multi-quadratic fields, including explicit leading coefficients and extensions to totally real cases.

Findings

Asymptotic formula for multi-quadratic fields with bounded discriminant

Explicit calculation of the leading coefficient

Extension to totally real multi-quadratic fields

Abstract

We prove an asymptotic formula for the number of multi-quadratic number fields of bounded discriminant with a power-saving error term. Furthermore, we explicitly calculate the leading coefficient and extend our result to totally real multi-quadratic number fields.