On certain infinite extensions of the rationals with Northcott property

DOI10.1007/s00605-009-0162-7zbMath1220.11133arXiv1205.2491OpenAlexW2017748372MaRDI QIDQ633263

Martin Widmer

Publication date: 31 March 2011

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.2491

zbMATH Keywords

heightalgebraic number fieldsNorthcott propertyinfinite field extensions

Mathematics Subject Classification ID

Algebraic field extensions (12F05) Heights (11G50) Algebraic numbers; rings of algebraic integers (11R04)

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Cites Work

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• On the properties of Northcott and of Narkiewicz for fields of algebraic numbers
• Lower bounds for height functions
• The Galois groups of the polynomials \(X^ n+aX\ell +b\)
• Polynomial mappings
• Cyclotomic Diophantine problems (Hilbert irreducibility and invariant sets for polynomial maps)
• A note on heights in certain infinite extensions of \(\mathbb Q\)
• Periodic points on an algebraic variety
• On polynomial transformations
• Number fields