Keywords:-

Keywords: Wigner-Ville distribution, Mobius function, Euler product, Absolute convergence, Riemann hypothesis

Article Content:-

Abstract

Wigner distribution is a tool for signal processing to obtain instantaneous spectrum of a signal. From which, another representation of the Euler product can be obtained for Dirichlet series of the Mobius function. From which, we can give the proof of the absolutely convergence of the Dirichlet series on the Mobius function which leads to the proof of the Riemann hypothesis.

References:-

References

Wigner,E. (1932) On the Quantum Correlations for Thermodynamic Equilibrium, Phys.Rev., Vol.40 , pp.749-759.

Ville,J. (1948) Theory et Application de la Notion de Signal Analytique, Cables et Transmissions, Vol.20A pp.61-77.

Claasen,T.A.M.C. and Mecklenbrauker,W.F.G. (1980) The Wigner Distribution- A Tool for Time-Frequency Signal Analysis (PART.I), Philips J.Res.35,pp. 217-250.

Paran, D.P. (1987) Exercices de theorie des nombres, Springer-Verlag Tokyo.

Henle,J.M, Kleinberg, E.M., Infinitesimal Calculus, Dover Publications, Inc, New York, 2003.

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Musha, T. (2022). Absolutely Convergence of the Dirichlet Series of the Mobius Function. International Journal Of Mathematics And Computer Research, 10(6), 2760-2765. https://doi.org/10.47191/ijmcr/v10i6.09