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arXiv · 2005.14110

Upper bounds on number fields of given degree and bounded discriminant

Robert J. Lemke Oliver·Frank Thorne
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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 $N_n(X) = O(X^{ c (\log n)^2})$ for an explicit constant $c$.

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Robert J. Lemke Oliver, Frank Thorne. 2020-05-28. Upper bounds on number fields of given degree and bounded discriminant. https://arxiv.org/abs/2005.14110

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