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IMPRIMITIVE PARAMETRIZATION OF ANALYTIC CURVES AND FACTORIZATIONS OF ENTIRE FUNCTIONS

Published online by Cambridge University Press:  30 October 2001

TUEN WAI NG
TUEN WAI NG
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Science, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB; ntw@dpmms.cam.ac.uk Current address: Institute of Mathematical Research, Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong; ntw@maths.hku.hk
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Abstract

Let f(z) and g(z) be transcendental entire functions. Fuchs and Song proved that if (f(z); g(z)) parametrizes some complex algebraic curve, then f and g must have a transcendental common right factor. The paper proves this result by a different method that also allows a similar result to be proved for some transcendental curves. This result is then used to solve some factorization problems of entire functions.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 385 - 394
Copyright
The London Mathematical Society 2001

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