An improved error term for counting $D_4$-quartic fields
We prove that the number of quartic fields $K$ with discriminant $|\Delta_K|\leq X$ whose Galois closure is $D_4$ equals $CX+O(X^{5/8+\varepsilon})$, improving the error term in a well-known result of Cohen, Diaz y Diaz, and Olivier. We prove an analogous result for counting quartic dihedral extensi...
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| Sprache: | eng |
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| Zusammenfassung: | We prove that the number of quartic fields $K$ with discriminant
$|\Delta_K|\leq X$ whose Galois closure is $D_4$ equals
$CX+O(X^{5/8+\varepsilon})$, improving the error term in a well-known result of
Cohen, Diaz y Diaz, and Olivier. We prove an analogous result for counting
quartic dihedral extensions over an arbitrary base field. |
|---|---|
| DOI: | 10.48550/arxiv.2307.14564 |