Asymptotic Bohr Radius for the Polynomials in One Complex Variable

Cheng Chu

Asymptotic Bohr Radius for the Polynomials in One Complex Variable

Complex Variables 2014-04-07 v2

Authors: Cheng Chu

Abstract

We consider the Bohr radius $R_n$ for the class of complex polynomials in one variable of degree at most $n$ . It was conjectured by R. Fournier in 2008 that $R_n={1\over 3}+{\pi^2\over {3n^2}}+o({1\over n^2})$ . We shall prove this conjecture is true in this paper.

Keywords

bohr phenomenon polynomial theory orthogonal polynomials

Cite

@article{arxiv.1403.6513,
  title  = {Asymptotic Bohr Radius for the Polynomials in One Complex Variable},
  author = {Cheng Chu},
  journal= {arXiv preprint arXiv:1403.6513},
  year   = {2014}
}

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