Jacob's ladders, heterogeneous quadrature formulae, big asymmetry and related formulae for the Riemann zeta-function

2014/01/13 by Jan Moser, Moser, Jan
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1401.2856

arxiv created 2014/01/13 · arxiv updated 2014/01/14

Abstract

In this paper we obtain as our main result new class of formulae expressing correlation integrals of the third-order in Z on disconnected sets \mathringG₁(x),\mathringG₂(y) by means of an autocorrelative sum of the second order in Z. Moreover, the distance of the sets \mathringG₁(x),\mathringG₂(y) from the set of arguments of autocorrelative sum is extremely big, namely ∼ Aπ(T), T→∞, where π(T) is the prime-counting function.

Related

• Jacob's ladders and the asymptotic formula for the integral of the eight order expression |ζ(1/2+i\vp₂(t))|⁴|ζ(1/2+it)|⁴
• Jacob's ladders and the nonlocal interaction of the function Z(t) with the function Z²(t) on the distance ∼ (1-c)π(t) for a collection of disconnected sets
• Jacob's ladders and the first asymptotic formula for the expression of the fifth order Z³[...]Z²(t) for the collection of disconnected sets
• Jacob's ladders and new class of integrals containing product of factors ζ²
• Jacob's ladders and the nonlocal interaction of the function Z²(t) with the function Z²(t) on the distance ∼ (1-c)π(t) for the collections of disconnected sets