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Positive exponential sums and odd polynomials

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


Puni tekst: engleski pdf 240 Kb

str. 35-53

preuzimanja: 535

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Sažetak

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.

Ključne riječi

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

Posjeta: 804 *