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Preprints of the Keldysh Institute of Applied Mathematics, 2012, 027, 17 pp.
(Mi ipmp45)
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On the classical Riemann zeta-function
L. D. Pustyl’nikov
Abstract:
We give a new construction of an operator acting in a Hilbert space such that the Riemann hypothesis on the zeros of the zeta-function is equivalent to the existence of an eigenvector for this operator with eigenvalue $-1$. We give also the construction of a dynamical system which turns out to be related to the Riemann hypothesis in the following way: there exists a complex zero of the zeta-function not lying on the critical line if and only if there is a periodic trajectory of order two having a special form for this dynamical system. The representation of the Riemann zeta-function by means of the infinite product of concrete matrices of order two lies on the basis of this construction.
Citation:
L. D. Pustyl’nikov, “On the classical Riemann zeta-function”, Keldysh Institute preprints, 2012, 027, 17 pp.
Linking options:
https://www.mathnet.ru/eng/ipmp45 https://www.mathnet.ru/eng/ipmp/y2012/p27
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Abstract page: | 256 | Full-text PDF : | 219 | References: | 45 |
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