Contribution of non integer integro-differential operators (NIDO) to the geometrical understanding of Riemann’s conjecture-(II)

Méhauté, Alain Le; Kaabouchi, A. El; Nivanen, Laurent

doi:10.1016/j.chaos.2006.05.093

Cited by 4 publications

(10 citation statements)

References 3 publications

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“…Both functions η are related to zeta Riemann function according to Above constraints involves j i p p = [11]. This relation leads to the second assertion, the relation between 0 ) ( = s ζ and the set of prime number P .…”

Section: ) Second Assertionmentioning

confidence: 97%

“…Now let us consider in detail both assertions. First let us recall some well established results about fractional dynamics associated with geodesics on opened punctuated torus [8,9,11]. We call Cole and Cole transfer function [12] a function Z(ν):…”

Section: ) Second Assertionmentioning

confidence: 99%

“…, may be analytically written as a part of a circle which centre is located out of the abscise axis [8,9]; This function is itself associated with a very simple fractional differential equation based on any intensive and extensive thermodynamic variables : U(t), I(t)…”

Section: ) Second Assertionmentioning

confidence: 99%

“…This proposal is based on the analytical parameterization of transfer function of non integer Integro-Diffential Equations [8,9,10] in the set of natural numbers when the tilling of the complex plane is reduced in the set of prime numbers [11].…”

Section: Introductionmentioning

confidence: 99%

“…The origin of the present work is an analogy between the pinning of the σ value on the fraction 1/2 and the pinning of phase angle upon the value 4 / π ϕ ± = for any dynamics which is under the control of 1/2-order Differential Equation [8,9,10]. Our analysis will be carried out in two major steps: …”

Section: Introductionmentioning

confidence: 99%

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Contribution of Non Integer Integro-Differential Operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

Méhauté

Kaabouchi

Nivanen

2006

IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics

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Section: ) Second Assertionmentioning

confidence: 97%

Section: ) Second Assertionmentioning

confidence: 99%

Section: ) Second Assertionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Contribution of Non Integer Integro-Differential Operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

Méhauté

Kaabouchi

Nivanen

2006

IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics

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Riemann’s conjecture and a fractional derivative

Méhauté

Kaabouchi

Nivanen

2010

Computers & Mathematics with Applications

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Role of Riemann's and Goldbach's hypotheses in the behaviour of complex systems:Introduction to the concept of "Sciances"

Méhauté

Tayurskiı̆

2012

J. Phys.: Conf. Ser.

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Abstract. The authors have already established a bi univocal correspondence betweenRiemann zeta functions and dynamic processes under the control of integro-differential operator of non-integer complex order. We recall that the Riemann zeta function can then be related to hyperbolic geodesics whose angles at the boundary are determined by the real part of the power laws that define the Riemann series. It is suggested that Riemann's conjecture can be reduced to a geometrical phase transition with a reduction of the parameter of order resulting from the combination of a pair symmetries associated with a quasi-self similarity of geodetics. The well-known relationship with the set of prime numbers must be considered as the result of the local existence of stationary 'state' in the dynamics. The work is focused on the 'non stationary' behaviour of Riemann zeta function. It is shown that the main characteristic of the dynamics of complex systems may be associated to a hybridizing between a pair of states and/or processes able to give a geometrical status to the concept of the time and equally to the concept of energy. It is based on the mirror properties of complementary zeta function. It is shown also that the set of prime numbers, which controls the transitions between 'states', is the simplest form of the complexity. This analysis suggests the existence of a mathematical relationship between Riemann's and Goldbach's hypothesis. Such relationship would be the base of an extension of the principles of the science for the analysis of the complexity. According to previous proposal we name this extension that enlarges the principles of the science: sciance with 'a'.

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Contribution of non integer integro-differential operators (NIDO) to the geometrical understanding of Riemann’s conjecture-(II)

Cited by 4 publications

References 3 publications

Contribution of Non Integer Integro-Differential Operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

Contribution of Non Integer Integro-Differential Operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

Riemann’s conjecture and a fractional derivative

Role of Riemann's and Goldbach's hypotheses in the behaviour of complex systems:Introduction to the concept of "Sciances"

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