On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation

2008/12/28 by Akinari Hoshi, Hoshi, Akinari, Katsuya Miyake +1
Mathematics · #11R16 #11R20 #12E25 #12F10 #12F12 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11R16 #msc:11R20 #msc:12E25 #msc:12F10 #msc:12F12

paper · pdf · doi:10.48550/arxiv.0812.4807

32 pages, 6 tables, to appear in Comment. Math. Univ. St. Pauli

arxiv created 2009/06/24 · arxiv updated 2009/12/01

Abstract

Let k be a field of characteristic ≠ 2. We give an answer to the field intersection problem of quartic generic polynomials over k via formal Tschirnhausen transformation and multi-resolvent polynomials.

Related

• On the field intersection problem of generic polynomials: a survey
• On the field intersection problem of solvable quintic generic polynomials
• A geometric framework for the subfield problem of generic polynomials via Tschirnhausen transformation
• On the simplest quartic fields and related Thue equations
• G.N. Chebotarev's "On the Problem of Resolvents"