The study establishes asymptotic formulae for biquadratic number fields in quaternionic and dihedral extensions, suggesting new insights into Galois theory.
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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Gaudet et al. (2025) studied this question.
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