An elliptic analogue of the Franklin-Schneider theorem

A. Bijlsma

An elliptic analogue of the Franklin-Schneider theorem

A. Bijlsma

Department of Mathematics and Computer Science

Research output: Contribution to journal › Article › Academic › peer-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 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

Fingerprint Dive into the research topics of 'An elliptic analogue of the Franklin-Schneider theorem'. Together they form a unique fingerprint.

Cite this

@article{66f0eccfbf28457dbd47b38a3d84a208,

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.",

author = "A. Bijlsma",

year = "1980",

language = "English",

volume = "2",

pages = "101--116",

journal = "Annales de la Facult{\'e} des Sciences de Toulouse. S{\'e}rie V",

issn = "0240-2963",

number = "2",

}

TY - JOUR

T1 - An elliptic analogue of the Franklin-Schneider theorem

AU - Bijlsma, A.

PY - 1980

Y1 - 1980

N2 - 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.

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

VL - 2

SP - 101

EP - 116

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

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

SN - 0240-2963

IS - 2

ER -