4 papers · 1 filter
Smale's mean value constant and admissible univalent Blaschke pairs
Aneesh Jatar, Tuen Wai Ng
Let be the class of polynomials of degree at least with , , let and let $\mathcal{M}=\sup_{P\in\mathcal{P}}S(P)…
Smale's Mean Value Conjecture and its Dual Conjecture for Complex Polynomials
Aneesh Jatar, Tuen Wai Ng
For the purposes of proving Smale's mean value conjecture, one may restrict consideration to an explicitly described family of so-called Schlicht normalized polynomials. For Schlic…
A Uniqueness Theorem for Holomorphic Mappings in the Disk Sharing Totally Geodesic Hypersurfaces
Jiaxing Huang, Tuen Wai Ng
In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces wit…
Higher Order, Polar and Sz.-Nagy's Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle
Pak-Leong Cheung, Tuen Wai Ng, Jonathan Tsai +1
For random polynomials with i.i.d. (independent and identically distribu-ted) zeros following any common probability distribution with support contained in the unit circle, the…