Jacob's ladders and the asymptotically approximate solutions of a nonlinear diophantine equation

Abstract

The nonlinear equation which is connected with the main term of the Hardy-Littlewood formula for ${\zeta }^2(1/2+it)$ is studied. In this direction I obtain the fine results which cannot be reached by published methods of Balasubramanian, Heath-Brown and Ivic in the field of the Hardy-Littlewood integral.

References in corpus (5)

• Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integral
• Jacob's ladders and the multiplicative asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral
• Jacob's ladders and the quantization of the Hardy-Littlewood integral
• Jacob's ladders and the first asymptotic formula for the expression of the fifth order $Z^3[...]{\hat{Z}}^2(t)$ for the collection of disconnected sets
• Jacob's ladders and the almost exact asymptotic representation of the Hardy-Littlewood integral

Cited by in corpus (5)

• Jacob's ladders and new orthogonal systems generated by Jacobi polynomials
• Jacob's ladders, Bessel's functions and the asymptotic solutions of a new class of nonlinear integral equations
• Jacob's ladders and some nonlinear integral equations connected with the Poisson-Lobachevsky integral
• Jacob's ladders and some new consequences from A. Selberg's formula
• Jacob's ladders and the ${\tilde{Z}}^2$-transformation of a polynomials in $\ln \vp_1(t)$