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Matematicheskie Zametki, 2004, Volume 76, Issue 5, Pages 688–700
DOI: https://doi.org/10.4213/mzm143 (Mi mzm143) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Turán Extremal Problem for Periodic Functions with Small Support and Its Applications

D. V. Gorbachev, A. S. Manoshina

Tula State University
Full-text PDF (236 kB) Citations (16)
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DOI: https://doi.org/10.4213/mzm143
Abstract: We study a Turán extremal problem on the largest mean value of a 1-periodic even function with nonnegative Fourier coefficients, fixed value at zero, and support on a closed interval $[-h,h]$, $0<h\le1/2$. We show how the solution of this extremal problem for rational numbers $h=p/q$ is related to the solution of two finite-dimensional problems of linear programming. The solution of the Turán problem for rational numbers $h$ of the form $2/q$, $3/q$, $4/q$, is obtained. Applications of the Turán problem to analytic number theory are given.
Received: 23.12.2003
English version:
Mathematical Notes, 2004, Volume 76, Issue 5, Pages 640–652
DOI: https://doi.org/10.1023/B:MATN.0000049663.45427.0f
Bibliographic databases:
UDC: 517.97
Language: Russian
Citation: D. V. Gorbachev, A. S. Manoshina, “Turán Extremal Problem for Periodic Functions with Small Support and Its Applications”, Mat. Zametki, 76:5 (2004), 688–700; Math. Notes, 76:5 (2004), 640–652
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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