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

By J. Moser. 2011

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AbstractIn 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.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6899115f05051bd12d814af0408e7741dd31f468