An elliptic analogue of the Franklin-Schneider theorem

A. Bijlsma

An elliptic analogue of the Franklin-Schneider theorem

A. Bijlsma

Mathematics and Computer Science

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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 language	English
Pages (from-to)	101-116
Number of pages	17
Journal	Annales de la Faculté des Sciences de Toulouse. Série V
Volume	2
Issue number	2
Publication status	Published - 1980

Cite this

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title = "An elliptic analogue of the Franklin-Schneider theorem",

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.",

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AB - 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.

M3 - Article

SN - 0240-2963

VL - 2

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JO - Annales de la Faculté des Sciences de Toulouse. Série V

JF - Annales de la Faculté des Sciences de Toulouse. Série V

IS - 2

ER -

An elliptic analogue of the Franklin-Schneider theorem

Abstract

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