|
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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm8816https://doi.org/10.4213/mzm8816 https://www.mathnet.ru/eng/mzm/v88/i3/p446
|
|