English

Bohr's power series theorem in several variables

Complex Variables 2008-02-03 v1

Abstract

Generalizing a classical one-variable theorem of Harald Bohr, we show that if an n-variable power series has modulus less than 1 in the unit polydisc, then the sum of the moduli of the terms is less than 1 in the polydisc of radius 1/(3*n^{1/2}).

Keywords

Cite

@article{arxiv.math/9606203,
  title  = {Bohr's power series theorem in several variables},
  author = {Harold P. Boas and Dmitry Khavinson},
  journal= {arXiv preprint arXiv:math/9606203},
  year   = {2008}
}
R2 v1 2026-07-22T17:56:12.760Z