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Cyclicity of zeros of families of analytic functions

Authors:	Email author" target="_blank">Alexander?Brudnyi Email author

Institution:	(1) Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

Abstract:	Let $\{f _{\lambda}\}$ be a family of holomorphic functions in the unit disk $\mathbb{D} \subset \mathbb{C}$ , which are also holomorphic in a parameter $\lambda \in V \subset \mathbb{C}^{n}$ . We express cyclicity (=generalized multiplicity) of a zero of $f _{\lambda}$ at $0 \in \mathbb{D}$ via some algebraic characteristics of the ideal generated by the Taylor coefficients of $f _{\lambda}$ . As an example we estimate the cyclicity of the family of generalized exponential polynomials.

Keywords:	((no ))
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