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. 
@article{TM_2012_276_a16,
     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},
     publisher = {mathdoc},
     volume = {276},
     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/