The Sidon constant for homogeneous polynomials

Joaquim Ortega-Cerdà; Myriam Ounaïes; Kristian Seip

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arXiv · 0903.1455

The Sidon constant for homogeneous polynomials

Joaquim Ortega-Cerdà·Myriam Ounaïes·Kristian Seip

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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).

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Joaquim Ortega-Cerdà, Myriam Ounaïes, Kristian Seip. 2009-03-08. The Sidon constant for homogeneous polynomials. https://arxiv.org/abs/0903.1455

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