Upper bounds on number fields of given degree and bounded discriminant
type: Item
instance of: scholarly article
title: Upper bounds on number fields of given degree and bounded discriminant
zbMATH Open document ID: 1504.11121
DOI: 10.1215/00127094-2022-0046
author: Robert J. Lemke Oliver
author: Frank Thorne
published in: Duke Mathematical Journal
publication date: 2022-10-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/2005.14110
review text: The authors give an upper bound for the number \(N_n(X)\) of number fields of degree \(n\) with discriminant bounded by \(X\): \(N_n(X) =O(X^{c(\log n)^2})\) for an explicit constant \(c\). The authors improve previous results of many authors. Their strategy follows the ideas of \textit{J. S. Ellenberg} and \textit{A. Venkatesh} [Ann. Math. (2) 163, No. 2, 723--741 (2006; Zbl 1099.11068)], and of \textit{J.-M. Couveignes} [Ann. Math. (2) 192, No. 2, 487--497 (2020; Zbl 1454.11190)].
reviewed by: Claude Levesque
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 7608258
zbMATH Keywords: arithmetic statistics
zbMATH Keywords: number field counting
describes a project that uses: PARI/GP
MaRDI profile type: Publication
OpenAlex ID: W3031380322
arXiv ID: 2005.14110
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description: scientific article