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arXiv · 2506.21522

Counting biquadratic number fields with quaternionic and dihedral extensions

Louis M. Gaudet·Siman Wong
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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.

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Louis M. Gaudet, Siman Wong. 2025-06-26. Counting biquadratic number fields with quaternionic and dihedral extensions. https://arxiv.org/abs/2506.21522

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