Jacob’s ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations
Tóm tắt
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.
Tài liệu tham khảo
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