Geodesic
Jacob's ladders, interactions between $\zeta $-oscillating systems, and a $\zeta $-analogue of an elementary trigonometric identity
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 203-218

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In our previous papers, within the theory of the Riemann zeta-function we have introduced the following notions: Jacob's ladders, oscillating systems, $\zeta $-factorization, metamorphoses, etc. In this paper we obtain a $\zeta $-analogue of an elementary trigonometric identity and other interactions between oscillating systems.
Keywords: Riemann zeta-function. 
@article{TM_2017_299_a12,
     author = {Jan Moser},
     title = {Jacob's ladders, interactions between $\zeta $-oscillating systems, and a $\zeta $-analogue of an elementary trigonometric identity},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {203--218},
     publisher = {mathdoc},
     volume = {299},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_299_a12/}
}
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Jan Moser. Jacob's ladders, interactions between $\zeta $-oscillating systems, and a $\zeta $-analogue of an elementary trigonometric identity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 203-218. http://geodesic.mathdoc.fr/item/TM_2017_299_a12/