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

2015/06/01 by Jan Moser, Moser, Jan · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #advanced mathematical theories #math.CA

paper · pdf · doi:10.48550/arxiv.1506.00442

arxiv created 2015/06/01 · openalex publication_date 2015/06/01 · arxiv updated 2015/06/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 σ=\frac 12 into a butterfly (=infinite series of M" obius functions in the region of absolute convergence σ>1).

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