Jacob's ladders, Riemann's oscillators, quotient of two oscillating multiforms and set of metamorphoses of this system

Abstract

In this paper we introduce complicated oscillating system, namely quotient of two multiforms based on Riemann-Siegel formula. We prove that there is an infinite set of metamorphoses of this system (=chrysalis) on critical line $\sigma =\frac{1}{2}$ into a butterfly (=infinite series of M\" obius functions in the region of absolute convergence $\sigma >1$).

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