Geodesic
Jacob's ladders, the structure of the Hardy–Littlewood integral and some new class of nonlinear integral equations
Informatics and Automation, Number theory, algebra, and analysis, Tome 276 (2012), pp. 213-226 
Jan Moser. Jacob's ladders, the structure of the Hardy–Littlewood integral and some new class of nonlinear integral equations. Informatics and Automation, Number theory, algebra, and analysis, Tome 276 (2012), pp. 213-226. http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a16/
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     author = {Jan Moser},
     title = {Jacob's ladders, the structure of the {Hardy{\textendash}Littlewood} integral and some new class of nonlinear integral equations},
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     year = {2012},
     volume = {276},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a16/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we obtain new formulae for short and microscopic parts of the Hardy–Littlewood integral, and the first asymptotic formula for the sixth-order expression $|\zeta(\frac12+i\varphi _1(t))|^4|\zeta(\frac 12+it)|^2$. These formulae cannot be obtained in the theories of Balasubramanian, Heath-Brown and Ivić.

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