The Library
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
|
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]](http://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
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
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: |
|
||||||||||||||||||
| 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: |
|
||||||||||||||||||
| Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
