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ON ℚ-DERIVED POLYNOMIALS

Published online by Cambridge University Press:  20 January 2009

E. V. Flynn
E. V. Flynn
Affiliation:
Department of Mathematical Sciences, Mathematics and Oceanography Building, University of Liverpool, Peach Street, Liverpool L69 7ZL, UK
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Abstract

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It is known that ℚ-derived univariate polynomials (polynomials defined over ℚ, with the property that they and all their derivatives have all their roots in ℚ) can be completely classified subject to two conjectures: that no quartic with four distinct roots is ℚ-derived, and that no quintic with a triple root and two other distinct roots is ℚ-derived. We prove the second of these conjectures.

AMS 2000 Mathematics subject classification: Primary 11G30

Keywords

genus 2Jacobianscoveringsℚ-derived
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 103 - 110
Copyright
Copyright © Edinburgh Mathematical Society 2001