Cyclicity and Maximal Multiplicity for Zeros of Families of Analytic Functions

Details Cyclicity and Maximal Multiplicity for Zeros of Families of Analytic Functions Cyclicity and Maximal Multiplicity for Zeros of Families of Analytic Functions

2002-05-09

arxiv.org/abs/math/0205096v1

Mathematics

Complex Variables

11 pages

Scientific paper

Let f_{\lambda} be a family of holomorphic functions in the unit disk,
holomorphic in parameter \lambda\in U\subset\C^{n}. We estimate the number of
zeros of f_{\lambda} in a smaller disk via some characteristic of the ideal
generated by Taylor coefficients of f_{\lambda}. Our estimate is locally sharp
and improve the previous estimate obtained by Roytwarf and Yomdin.

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