Inequalities for polynomials with real critical values
Abstract
Under certain geometrical constraints on the polynomials with real critical values, we give lower and upper estimates of the moduli of the polynomial and of its derivative independent of the degree of this polynomial. As a corollary, we refine Hinkkanen and Kayumov's estimate for $\min\{|P(\zeta)/\zeta|\colon P'(\zeta)=0\}$ for polynomials $P$, $P(0)=0$, $P'(0)=1$, with real critical points.
Fields of Study & Subjects
Mathematical functions and polynomials
Geometry and complex manifolds
Analytic Number Theory Research
Publication details
- Journal / source
- Izvestiya Mathematics
- Publisher
- Steklov Mathematical Institute
- Volume
- 90
- Issue
- 3
- Pages
- 515–529
- Publication date
- 1 January 2026
- Language
- EN