Jacob's ladders and the ${\tilde{Z}}^2$-transformation of a polynomials in $\ln \vp_1(t)$

Abstract

It is proved in this paper that there is a nonlocal asymptotic splitting (in the integral sense) of the function $Z^4(t)$ into two factors. The corresponding formula cannot be obtained in the known theories of Balasubramanian, Heath-Brown and Ivic.

References in corpus (6)

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