Counting biquadratic number fields with quaternionic and dihedral extensions
Number Theory
2025-06-27 v1
Abstract
We establish asymptotic formulae for the number of biquadratic number fields of bounded discriminant that can be embedded into a quaternionic or a dihedral extension. To prove these results, we express the solvability of these inverse Galois problems in terms of Hilbert symbols, and then apply a method of Heath-Brown to bound sums of linked quadratic characters.
Cite
@article{arxiv.2506.21522,
title = {Counting biquadratic number fields with quaternionic and dihedral extensions},
author = {Louis M. Gaudet and Siman Wong},
journal= {arXiv preprint arXiv:2506.21522},
year = {2025}
}
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37 pages