Cyclicity and Maximal Multiplicity for Zeros of Families of Analytic Functions
arXiv:math/0205096
Abstract
Let f_λ be a family of holomorphic functions in the unit disk, holomorphic in parameter λ\in U\subset\C^{n}. We estimate the number of zeros of f_λ in a smaller disk via some characteristic of the ideal generated by Taylor coefficients of f_λ. Our estimate is locally sharp and improve the previous estimate obtained by Roytwarf and Yomdin.
11 pages