Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Enumerative Galois theory for cubics and quartics

Tools
- Tools
+ Tools

Chow, Sam and Dietmann, Rainer (2020) Enumerative Galois theory for cubics and quartics. Advances in Mathematics, 372 . doi:10.1016/j.aim.2020.107282

[img]
Preview
PDF
WRAP-Enumerative-Galois-theory-cubics-quartic-Chow-2020.pdf - Published Version - Requires a PDF viewer.
Available under License Creative Commons Attribution 4.0.

Download (546Kb) | Preview
[img] PDF
WRAP-Enumerative-Galois-theory-cubics-quartics-Chow-2020.pdf - Accepted Version
Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer.

Download (1060Kb)
Official URL: https://doi.org/10.1016/j.aim.2020.107282

Request Changes to record.

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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of 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:
DateEvent
7 October 2020Published
27 July 2020Available
17 June 2020Accepted
Date of first compliant deposit: 29 June 2020
Volume: 372
DOI: 10.1016/j.aim.2020.107282
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/S00226X/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/S00226X/2Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/J018260/1Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
UNSPECIFIEDMathematisches Forschungsinstitut Oberwolfachhttp://viaf.org/viaf/126009808/#Mathematisches_Forschungsinstitut_Oberwolfach.
DMS-1440140National Science Foundationhttp://dx.doi.org/10.13039/501100008982
Related URLs:
  • Publisher

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item
twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us