Counting biquadratic number fields with quaternionic and dihedral extensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912451897851904 |
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| author | Gaudet, Louis M. Wong, Siman |
| author_facet | Gaudet, Louis M. Wong, Siman |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting biquadratic number fields with quaternionic and dihedral extensions Gaudet, Louis M. Wong, Siman Number 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. |
| title | Counting biquadratic number fields with quaternionic and dihedral extensions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.21522 |