An elliptic analogue of the Franklin-Schneider theorem

A. Bijlsma

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Let p be a Weierstrass elliptic function with algebraic invariants g2 and g3. Let a and b be complex numbers such that a and b are not among the poles of p. A lower bound is given for the simultaneous approximation of p(a), b and p(ab) by algebraic numbers, expressed in their heights and degrees. By a counterexample it is shown that a certain hypothesis on the numbers beta approximating b is necessary.
Original languageEnglish
Pages (from-to)101-116
Number of pages17
JournalAnnales de la Faculté des Sciences de Toulouse. Série V
Volume2
Issue number2
Publication statusPublished - 1980

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Weierstrass Function
Simultaneous Approximation
Algebraic number
Elliptic function
Complex number
Counterexample
Pole
Lower bound
Analogue
Invariant
Necessary
Theorem

Cite this

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An elliptic analogue of the Franklin-Schneider theorem. / Bijlsma, A.

In: Annales de la Faculté des Sciences de Toulouse. Série V, Vol. 2, No. 2, 1980, p. 101-116.

Research output: Contribution to journalArticleAcademicpeer-review

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