Positive exponential sums and odd polynomials

Marina Nincevic; Sinisa Slijepcevic

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arXiv · 1301.3655

Positive exponential sums and odd polynomials

Marina Nincevic·Sinisa Slijepcevic

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Abstract

Given an odd integer polynomial f(x) of a degree k >=3, we construct a non-negative valued, normed trigonometric polynomial with the spectrum in the set of integer values of f(x) not greater than n, and a small free coefficient a_{0}=O((\log n)^{-1/k}). This gives an alternative proof for the maximal possible cardinality of a set A, so that A-A does not contain an element of f(x). We also discuss other interpretations and an ergodic characterization of that bound.

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Marina Nincevic, Sinisa Slijepcevic. 2013-01-16. Positive exponential sums and odd polynomials. https://arxiv.org/abs/1301.3655

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