On the field intersection problem of solvable quintic generic polynomials

2008/04/30 by Akinari Hoshi, Hoshi, Akinari, Katsuya Miyake +1 · 1 citation
Computer Science · Mathematics · #11R16 #11R20 #12F10 #12F12 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11R16 #msc:11R20 #msc:12F10 #msc:12F12

paper · pdf · doi:10.48550/arxiv.0804.4875

27 pages, 4 tables, to appear in Int. J. Number Theory

openalex publication_date 2008/04/30 · arxiv created 2009/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a general method of the field intersection problem of generic polynomials over an arbitrary field k via formal Tschirnhausen transformation. In the case of solvable quintic, we give an explicit answer to the problem by using multi-resolvent polynomials.

Citations

• Classifying Brumer's quintic polynomials by weak Mordell-Weil groups

Cited by

• On the field intersection problem of generic polynomials: a survey

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