On the field intersection problem of generic polynomials: a survey

2008/10/02 by Akinari Hoshi, Hoshi, Akinari, Katsuya Miyake +1
Computer Science · Mathematics · #11R16 #11R20 #12E25 #12F10 #12F12 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.NT #math.RA #msc:11R16 #msc:11R20 #msc:12E25 #msc:12F10 #msc:12F12

paper · pdf · doi:10.48550/arxiv.0810.0382

To appear in RIMS Kokyuroku Bessatsu. 17 pages

openalex publication_date 2008/10/02 · arxiv created 2009/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a field of characteristic ≠ 2. We survey a general method of the field intersection problem of generic polynomials via formal Tschirnhausen transformation. We announce some of our recent results of cubic, quartic and quintic cases the details of which are to appear elsewhere. In this note, we give an explicit answer to the problem in the cases of cubic and dihedral quintic by using multi-resolvent polynomials.

Citations

• On the field intersection problem of solvable quintic generic polynomials

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