New consequences of the Riemann-Siegel formula and a law of asymptotic equality of signum-areas of Z(t) function
Abstract
In this paper we obtain the first mean-value theorems for the function Z(t) on some disconnected sets. Next, we obtain a geometric law that controls chaotic behavior of the graph of the function Z(t). This paper is the English version of the papers 8 and 9, except of the Appendix that connects our results with the theory of Jacob's ladders, namely new third-order formulae have been obtained.
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