Abstract
The Riemann Zeta-function is related to the fundamental law of distribution of the primes and it is known that a very important problem in mathematics and related fields is connected with a proof of the Riemann Hypothesis (RH). The RH has connections with many areas: arithmetics, quantum theory, phase transition, dynamical systems, chaos and cryptografy. In this note we first recall some properties of the Zeta-function and briefly notice on some results reported in recent pioneering works. We then present our numerical treatment concerning the Riemann-Mangoldt function calculated on the primes up to 2.15 billions and we give a new estimation of the RiemannMangoldt constant C. Finally we develope a formal perturbation expansion and analyse it in a first order approximation. The values for the low zeroes of the Zeta-function are also given.
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Merlini, D., Rusconi, L., Bernasconi, A. (2002). Complex Aspects of the Riemann Hypothesis: a Computational Approach. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8119-7_32
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DOI: https://doi.org/10.1007/978-3-0348-8119-7_32
Publisher Name: Birkhäuser, Basel
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