The density of discriminants of quintic rings and fields
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Publication:624913
DOI10.4007/ANNALS.2010.172.1559zbMATH Open1220.11139arXiv1005.5578OpenAlexW2950749849WikidataQ30053312 ScholiaQ30053312MaRDI QIDQ624913
Author name not available (Why is that?)
Publication date: 11 February 2011
Published in: (Search for Journal in Brave)
Abstract: We determine, asymptotically, the number of quintic fields having bounded discriminant. Specifically, we prove that the asymptotic number of quintic fields having absolute discriminant at most X is a constant times X. In contrast with the quartic case, we also show that a density of 100% of quintic fields, when ordered by absolute discriminant, have Galois closure with full Galois group . The analogues of these results are also proven for orders in quintic fields. Finally, we give an interpretation of the various constants appearing in these theorems in terms of local masses of quintic rings and fields.
Full work available at URL: https://arxiv.org/abs/1005.5578
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