15 October 2022 Upper bounds on number fields of given degree and bounded discriminant
Robert J. Lemke Oliver, Frank Thorne
Author Affiliations +
Duke Math. J. 171(15): 3077-3087 (15 October 2022). DOI: 10.1215/00127094-2022-0046

Abstract

Let Nn(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 Nn(X), finding that Nn(X)=O(Xc(logn)2) for an explicit constant c.

Citation

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Robert J. Lemke Oliver. Frank Thorne. "Upper bounds on number fields of given degree and bounded discriminant." Duke Math. J. 171 (15) 3077 - 3087, 15 October 2022. https://doi.org/10.1215/00127094-2022-0046

Information

Received: 18 June 2020; Revised: 24 August 2021; Published: 15 October 2022
First available in Project Euclid: 30 August 2022

MathSciNet: MR4497223
zbMATH: 1504.11121
Digital Object Identifier: 10.1215/00127094-2022-0046

Subjects:
Primary: 11R29

Keywords: arithmetic statistics , number field counting

Rights: Copyright © 2022 Duke University Press

Vol.171 • No. 15 • 15 October 2022
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