Jacob's ladders and the first asymptotic formula for the expression of the fifth order Z3[...]Z2(t) for the collection of disconnected sets
Abstract
It is shown in this paper that there is a fine correlation of the fifth order between the values Z[φ(t)/2+1]Z[φ(t)/2+2]Z[φ(t)/2+3] and Z2(t) which correspond to two collections of disconnected sets. This new asymptotic formula cannot be obtained within known theories of Balasubramanian, Heath-Brown and Ivic.
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