Geodesic
Jacob's ladders, the structure of the Hardy--Littlewood integral and some new class of nonlinear integral equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 213-226.

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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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     author = {Jan Moser},
     title = {Jacob's ladders, the structure of the {Hardy--Littlewood} integral and some new class of nonlinear integral equations},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {213--226},
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     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_276_a16/}
}
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Jan Moser. Jacob's ladders, the structure of the Hardy--Littlewood integral and some new class of nonlinear integral equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 213-226. http://geodesic.mathdoc.fr/item/TM_2012_276_a16/

[1] Fok V.A., Teoriya prostranstva, vremeni i tyagoteniya, Gostekhizdat, M., 1955; Fock V., The theory of space, time and gravitation, Pergamon Press, Oxford, 1963 | MR | Zbl

[2] Hardy G.H., Littlewood J.E., “Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes”, Acta math., 41:1 (1918), 119–196 | DOI | MR

[3] Hardy G.H., Littlewood J.E., “The approximate functional equation in the theory of the zeta-function, with applications to the divisor-problems of Dirichlet and Piltz”, Proc. London Math. Soc. Ser. 2, 21 (1922), 39–74 | DOI | MR

[4] Ingham A.E., “Mean-value theorems in the theory of the Riemann zeta-function”, Proc. London Math. Soc. Ser. 2, 27 (1927), 273–300 | DOI | MR | Zbl

[5] Ivić A., The Riemann zeta-function: The theory of the Riemann zeta-function with applications, J. Wiley Sons, New York, 1985 | MR | Zbl

[6] Karatsuba A.A., Complex analysis in number theory, CRC Press, Boca Raton, FL, 1995 | MR | Zbl

[7] Littlewood J.E., “Two notes on the Riemann zeta-function”, Proc. Cambridge Philos. Soc., 22 (1924), 234–242 | DOI | Zbl

[8] Moser J., “Jacob's ladders and the almost exact asymptotic representation of the Hardy–Littlewood integral”, Math. Notes, 88 (2010), 414–422 | DOI | DOI | MR | Zbl

[9] Selberg A., “Contributions to the theory of the Riemann zeta-function”, Arch. Math. Naturvid., 48:5 (1946), 89–155 | MR | Zbl

[10] Titchmarsh E.C., The theory of the Riemann zeta-function, Clarendon Press, Oxford, 1951 | MR | Zbl