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Research Article Open access CC BY 4.0

Wigner Distribution Analysis Applied to Lehmer’s Conjecture on the Ramanujan tau Function

Takaaki Musha

Asian Research Journal of Mathematics · pp. 19–28 · Published 25 Sep 2021

10.9734/arjom/2021/v17i730315

Abstract

Wigner distribution is a tool for signal processing to obtain instantaneous spectrum of a signal. By using Wigner distribution analysis, another representation of the Euler product can be obtained for Dirichlet series of the Ramanujan tau function. From which, it can be proved that the Ramanujan tau function never become zero for all numbers.

Wigner-Ville distribution lehmer’s conjecture ramanujan tau function ramanujan’s zeta function euler product

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