On the Rigidity of the Roots of Power Series With Constrained Coefficients
Abstract
Abstract Here we consider the set $\Sigma _{S}$ of roots of power series whose coefficients lie in a given set $S$ and how such sets of roots vary as the set $S$ varies. We give an estimate of the depth that complex roots can reach into the disk, offer some criterion for the set of roots to be connected or disconnected, and show that for two finite symmetric sets $S$ and $T$ of integers containing $1$, if $\Sigma _{S} = \Sigma _{T}$ then all of their elements between $1$ and $2\sqrt{\max (S)}+1$ must agree.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 9
- Publication date
- 16 April 2026
- Language
- EN