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Matematicheskie Zametki, 2010, Volume 88, Issue 3, Pages 446–455
DOI: https://doi.org/10.4213/mzm8816 (Mi mzm8816) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Jacob's Ladders and the Almost Exact Asymptotic Representation of the Hardy–Littlewood Integral

J. Moser

Comenius University
Full-text PDF (490 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm8816
Abstract: In this paper we introduce a nonlinear integral equation such that the system of global solutions to this equation represents the class of a very narrow beam as $T\to\infty$ (an analog of the laser beam) and this sheaf of solutions leads to an almost-exact representation of the Hardy–Littlewood integral (1918). The accuracy of our result is essentially better than the accuracy of related results of Balasubramanian, Heath–Brown, and Ivic.
Keywords: Hardy–Littlewood integral, Riemann zeta function, Gauss logarithmic integral, nonlinear integral equation, Jacob's ladder, Bonnet's mean-value theorem.
Received: 21.04.2009
English version:
Mathematical Notes, 2010, Volume 88, Issue 3, Pages 414–422
DOI: https://doi.org/10.1134/S0001434610090142
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: J. Moser, “Jacob's Ladders and the Almost Exact Asymptotic Representation of the Hardy–Littlewood Integral”, Mat. Zametki, 88:3 (2010), 446–455; Math. Notes, 88:3 (2010), 414–422
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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