LINEAR DIOPHANTINE INEQUALITIES APPLIED TO GENERALIZED FABER POLYNOMIALS

Linear Diophantine Inequalities Applied to Generalized Faber Polynomials.

Derivatives of Faber Polynomials and Markov Inequalities

We study asymptotic behavior of the derivatives of Faber polynomials on a set with corners at the boundary. Our results have applications to the questions of sharpness of Markov inequalities for such sets. In particular, the found asymptotics are related to a general Markov-type inequality of Pommerenke and the associated conjecture of Erdős. We also prove a new bound for Faber polynomials on p...

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Diophantine m-tuples for linear polynomials

In this paper, we prove that there does not exist a set with more than 26 polynomials with integer coefficients, such that the product of any two of them plus a linear polynomial is a square of a polynomial with integer coefficients. 1991 Mathematics Subject Classification: 11D09.

Lattice Paths and Faber Polynomials

The rth Faber polynomial of the Laurent series f(t) = t + f0 + f1/t + f2/t + · · · is the unique polynomial Fr(u) of degree r in u such that Fr(f) = tr + negative powers of t. We apply Faber polynomials, which were originally used to study univalent functions, to lattice path enumeration.