English

The Sidon constant for homogeneous polynomials

Complex Variables 2009-03-10 v1

Abstract

The Sidon constant for the index set of nonzero m-homogeneous polynomials P in n complex variables is the supremum of the ratio between the l^1 norm of the coefficients of P and the supremum norm of P in D^n. We present an estimate which gives the right order of magnitude for this constant, modulo a factor depending exponentially on m. We use this result to show that the Bohr radius for the polydisc D^n is bounded from below by a constant times sqrt((log n)/n).

Keywords

Cite

@article{arxiv.0903.1455,
  title  = {The Sidon constant for homogeneous polynomials},
  author = {Joaquim Ortega-Cerdà and Myriam Ounaïes and Kristian Seip},
  journal= {arXiv preprint arXiv:0903.1455},
  year   = {2009}
}
R2 v1 2026-06-21T12:19:38.493Z