An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree

Manjul Bhargava, Arul Shankar, Xiaoheng Wang

Research output: Contribution to journalArticlepeer-review

Abstract

We prove an improvement on Schmidt's upper bound on the number of number fields of degree n and absolute discriminant less than X for 6 ≤ n ≤ 94. We carry this out by improving and applying a uniform bound on the number of monic integer polynomials, having bounded height and discriminant divisible by a large square, that we proved in a previous work [7].

Original languageEnglish (US)
Article number71
JournalForum of Mathematics, Sigma
Volume10
DOIs
StatePublished - Oct 10 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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