Upper bounds on number fields of given degree and bounded discriminant

By Robert J. Lemke Oliver, F. Thorne. Duke mathematical journal, 2020

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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 $c$.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/29912d8e4096f108800abb16dad68b50b5abba0c