Positive exponential sums and odd polynomials
Number Theory
2013-01-17 v1
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.
Cite
@article{arxiv.1301.3655,
title = {Positive exponential sums and odd polynomials},
author = {Marina Nincevic and Sinisa Slijepcevic},
journal= {arXiv preprint arXiv:1301.3655},
year = {2013}
}