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}
}