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Improved bounds on number fields of small degree

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arxiv 2204.01651 v4 pith:H5LZK64C submitted 2022-04-04 math.NT math.AG

Theresa C. Anderson , Ayla Gafni , Kevin Hughes , Robert J. Lemke Oliver , David Lowry-Duda , Frank Thorne , Jiuya Wang , Ruixiang Zhang This is my paper · ORCID
classification math.NTmath.AG
keywords numberfieldsbounddegreeupperarticlebestbounded
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abstract

We study the number of degree $n$ number fields with discriminant bounded by $X$. In this article, we improve an upper bound due to Schmidt on the number of such fields that was previously the best known upper bound for $6 \leq n \leq 94$.

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  1. Secondary terms in the first moment of $|{\rm Sel}_2(E)|$

    math.NT 2024-12 accept novelty 8.0 of 10

    For elliptic curves ordered by height, the first moment of |Sel2(E)| contains a secondary term of order X^{3/4}, with a power-saving error of size O(X^{3/4-1/3804+epsilon}).

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