Proceedings of the Steklov Institute of Mathematics

, Volume 299, Issue 1, pp 189–204 | Cite as

Jacob’s Ladders, Interactions between ζ-Oscillating Systems, and a ζ-Analogue of an Elementary Trigonometric Identity



In our previous papers, within the theory of the Riemann zeta-function we have introduced the following notions: Jacob’s ladders, oscillating systems, ζ-factorization, metamorphoses, etc. In this paper we obtain a ζ-analogue of an elementary trigonometric identity and other interactions between oscillating systems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Moser, “Jacob’s ladders and the almost exact asymptotic representation of the Hardy–Littlewood integral,” Mat. Zametki 88 (3), 446–455 (2010) [Math. Notes 88, 414–422 (2010)].MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Moser, “Jacob’s ladders, the structure of the Hardy–Littlewood integral and some new class of nonlinear integral equations,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 276, 213–226 (2012) [Proc. Steklov Inst. Math. 276, 208–221 (2012)].MathSciNetMATHGoogle Scholar
  3. 3.
    J. Moser, “Jacob’s ladders, reverse iterations and new infinite set of L 2-orthogonal systems generated by the Riemann ζ(\(\frac{1}{2} + it\))-function,” arXiv: 1402.2098 [math.CA].Google Scholar
  4. 4.
    J. Moser, “Jacob’s ladders, ζ-factorization and infinite set of metamorphoses of a multiform,” arXiv: 1501.07705v2 [math.CA].Google Scholar
  5. 5.
    J. Moser, “Jacob’s ladders, Riemann’s oscillators, quotient of two oscillating multiforms and set of metamorphoses of this system,” arXiv: 1506.00442 [math.CA].Google Scholar
  6. 6.
    J. Moser, “Jacob’s ladders, factorization, and metamorphoses as an appendix to the Riemann functional equation for ζ(s) on the critical line,” Sovrem. Probl. Mat. 23, 102–113 (2016) [Proc. Steklov Inst. Math. 296 (Suppl. 2), S92–S102 (2017)].CrossRefGoogle Scholar
  7. 7.
    J. Moser, “Jacob’s ladders, Z ζ,Q 2-transformation of real elementary functions and telegraphic signals generated by the power functions,” arXiv: 1602.04994 [math.CA].Google Scholar
  8. 8.
    C. L. Siegel, “Über Riemanns Nachlass zur analytischen Zahlentheorie,” Quell. Stud. Gesch. Math. Astron. Phys., Abt. B 2, 45–80 (1932).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Department of Mathematical Analysis and Numerical MathematicsComenius UniversityBratislavaSlovakia

Personalised recommendations