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Enumerative Galois theory for cubics and quartics
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Chow, Sam and Dietmann, Rainer (2020) Enumerative Galois theory for cubics and quartics. Advances in Mathematics, 372 . doi:10.1016/j.aim.2020.107282 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2020.107282
Abstract
We show that there are Oε(H1.5+ε) monic, cubic polynomials with integer coefficients bounded by H in absolute value whose Galois group is A3. We also show that the order of magnitude for D4 quartics is H2(log H)2, and that the respective counts for A4, V4, C4 are O(H2.91), O(H2 log H), O(H2 log H). Our work establishes that irreducible non-S3 cubic
polynomials are less numerous than reducible ones, and similarly in the
quartic setting: these are the first two solved cases of a 1936 conjecture made by van der Waerden
Item Type: | Journal Article | ||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Galois theory, Determinants, Polynomials, Measure theory | ||||||||||||||||||
Journal or Publication Title: | Advances in Mathematics | ||||||||||||||||||
Publisher: | Academic Press | ||||||||||||||||||
ISSN: | 0001-8708 | ||||||||||||||||||
Official Date: | 7 October 2020 | ||||||||||||||||||
Dates: |
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Volume: | 372 | ||||||||||||||||||
DOI: | 10.1016/j.aim.2020.107282 | ||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
Date of first compliant deposit: | 29 June 2020 | ||||||||||||||||||
Date of first compliant Open Access: | 31 July 2020 | ||||||||||||||||||
RIOXX Funder/Project Grant: |
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