On the field intersection problem of solvable quintic generic polynomials

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.

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

References in corpus (1)

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

Cited by in corpus (2)

• On the field intersection problem of generic polynomials: a survey
• A note on the field isomorphism problem of X^3+sX+s and related cubic Thue equations