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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 6, Pages 31–90 (Mi izv95)  

This article is cited in 3 scientific papers (total in 4 papers)

An estimate of the free term of a non-negative trigonometric polynomial with integer coefficients

A. S. Belova, S. V. Konyaginb

a Ivanovo State University
b M. V. Lomonosov Moscow State University

Abstract: We denote by $M_Z^{\downarrow}(n)$ (resp., $K_Z^{\downarrow}(n)$) the smallest value of $a_0$ that can occur in a non-negative trigonometric polynomial
$$ \sum_{k=0}^n a_k\cos(kx) $$
with non-negative integer coefficients $a_1\geqslant a_2\geqslant…\geqslant a_n$ such that $a_n\geqslant 1$ (resp., $\sum_{k=1}^n a_k=n$). We prove that for all natural numbers $n\geqslant 3$
$$ \dfrac{\ln^2 n}{\ln\ln n}\ll K_Z^\downarrow(n)\ll M_Z^\downarrow(n)\ll(\ln n)^3. $$


DOI: https://doi.org/10.4213/im95

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English version:
Izvestiya: Mathematics, 1996, 60:6, 1123–1182

Bibliographic databases:

Document Type: Article
MSC: 42A05
Received: 05.04.1996

Citation: A. S. Belov, S. V. Konyagin, “An estimate of the free term of a non-negative trigonometric polynomial with integer coefficients”, Izv. RAN. Ser. Mat., 60:6 (1996), 31–90; Izv. Math., 60:6 (1996), 1123–1182

Citation in format AMSBIB
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\by A.~S.~Belov, S.~V.~Konyagin
\paper An estimate of the free term of a~non-negative trigonometric polynomial with integer coefficients
\jour Izv. RAN. Ser. Mat.
\yr 1996
\vol 60
\issue 6
\pages 31--90
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\pages 1123--1182
\crossref{https://doi.org/10.1070/IM1996v060n06ABEH000095}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sergei V. Konyagin, Maxim M. Skriganov, Alexander V. Sobolev, “On a lattice point problem arising in the spectral analysis of periodic operators”, Mathematika, 50:1-2 (2003), 87  crossref  mathscinet  zmath  isi  elib  scopus
    2. Revesz S.G., “Turan's extremal problem on locally compact abelian groups”, Anal Math, 37:1 (2011), 15–50  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    4. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, K. S. Ryutin, I. D. Shkredov, “Sergei Vladimirovich Konyagin turns 60”, Proc. Steklov Inst. Math., 303 (2018), 1–9  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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