arXiv Analytics

Sign in

arXiv:2506.21522 [math.NT]AbstractReferencesReviewsResources

Counting biquadratic number fields with quaternionic and dihedral extensions

Louis M. Gaudet, Siman Wong

Published 2025-06-26Version 1

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.

Comments: 37 pages
Categories: math.NT
Related articles: Most relevant | Search more
arXiv:math/0301387 [math.NT] (Published 2003-01-31)
Class Groups of Dihedral Extensions
arXiv:1404.6091 [math.NT] (Published 2014-04-24)
Presentations for quaternionic $S$-unit groups
Ted Chinburg et al.
arXiv:1701.07864 [math.NT] (Published 2017-01-26)
Congruences for modular forms mod 2 and quaternionic $S$-ideal classes

Links

Toolbox