Upper bounds on number fields of given degree and bounded discriminant

DOI10.1215/00127094-2022-0046zbMATH Open1504.11121arXiv2005.14110OpenAlexW3031380322MaRDI QIDQ2093537

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Publication date: 27 October 2022

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Abstract: Let $N_n(X)$ denote the number of degree $n$ number fields with discriminant bounded by $X$. In this note, we improve the best known upper bounds on $N_n(X)$, finding that $N_n(X)=O(X^{c(logn{)}^2})$ for an explicit constant $c$.

Full work available at URL: https://arxiv.org/abs/2005.14110

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