# Asymptotics of Chebyshev Polynomials, IV. Comments on the Complex Case

## TL;DR

This paper discusses the asymptotic behavior of Chebyshev polynomials on complex compact sets, focusing on zero distribution and explicit norm bounds, advancing understanding of their complex case properties.

## Contribution

It provides new insights into the asymptotics of zeros and explicit norm bounds for Chebyshev polynomials in the complex setting, extending previous real-case results.

## Key findings

- Asymptotic zero distribution for Chebyshev polynomials in the complex plane
- Explicit Totik–Widom upper bounds on polynomial norms
- Comments on the differences between real and complex cases

## Abstract

We make a number of comments on Chebyshev polynomials for general compact subsets of the complex plane. We focus on two aspects: asymptotics of the zeros and explicit Totik--Widom upper bounds on their norms.