Original scientific paper

Positive exponential sums and odd polynomials

Marina Ninčević ; Department of Mathematics, Bijenička 30, Zagreb, Croatia
Siniša Slijepčević orcid.org/0000-0001-5600-0171 ; Department of Mathematics, Bijenička 30, Zagreb, Croatia

Abstract

Given an odd integer polynomial f(x) of a degree k >= 3,
we construct a non-negative valued, normed trigonometric polynomial with non-vanishing coefficients only at 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 of the bound for the maximal possible cardinality of a set of integers A, so that A − A does not contain an integer value of f(x). We also discuss other interpretations and an ergodic characterization of that bound.

Keywords

Positive exponential sums; van der Corput sets; correlative sets; recurrence; difference sets; Fejér’s kernel; positive definiteness

Hrčak ID:

127645

URI

https://hrcak.srce.hr/127645

Publication date:

30.9.2014.

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