A note on elliptic functions and approximation by algebraic numbers of bounded degree

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1983 Netherlands English Publisher:MathDoc/Centre MersenneJournal:Annales de la Faculté des sciences de Toulouse : Mathématiques, volume 5, pages 39-42 (eissn: 2258-7519,

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Authors: Bijlsma, A.;

doi: 10.5802/afst.587

A note on elliptic functions and approximation by algebraic numbers of bounded degree

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Abstract

Let p be a Weierstrass elliptic function with algebraic invariants g2 and g3. By a counterexample it is shown that lower bounds for the simultaneous approximation of p(a), b and p(ab) by algebraic numbers of bounded degree cannot be given without and added hypothesis on the numbers beta approximating b.

Country

Netherlands

Related Organizations

Utrecht University
Netherlands
Technical University Eindhoven
Netherlands

Keywords

Approximation by numbers from a fixed field, Weierstrass elliptic function, simultaneous approximation, Transcendence (general theory), approximation by algebraic numbers of bounded degree, Wiskunde en Informatica, transcendence

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