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Jacob’s ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations

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Abstract

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 \(\left| {\zeta \left( {\tfrac{1} {2} + i\phi _1 \left( t \right)} \right)} \right|^4 \left| {\zeta \left( {\tfrac{1} {2} + it} \right)} \right|^2\). These formulae cannot be obtained in the theories of Balasubramanian, Heath-Brown and Ivić.

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Authors and Affiliations

  1. Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská Dolina M105, 842 48, Bratislava, Slovakia

    Jan Moser

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  1. Jan Moser
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Correspondence to Jan Moser.

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Dedicated to the 75th anniversary of Anatolii Alekseevich Karatsuba

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Moser, J. Jacob’s ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations. Proc. Steklov Inst. Math. 276, 208–221 (2012). https://doi.org/10.1134/S0081543812010178

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  • DOI: https://doi.org/10.1134/S0081543812010178

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