Cyclicity of zeros of families of analytic functions (Q1430507)

The author considers a family \(\{f_\lambda\}\) of holomorphic functions in the unit disc \(D\) of the complex plane \(\mathbf{C}\), which are also holomorphic in a parameter \(\lambda\in V\), where \(V\) is an open set in \(\mathbf{C}^n\). To this end, the author expresses the cyclicity of a zero of \(f_\lambda\) at \(0\in D\), by using certain algebraic characteristics of the ideal generated by the Taylor coefficients of the function \(f_\lambda\). In addition, the author estimates the cyclicity of the family of generalized polynomials. The paper ends with some concluding remarks.