Wigner Distribution Analysis Applied to Lehmer’s Conjecture on the Ramanujan tau Function
Takaaki Musha *
Advanced Science, Technology Research Organization, Yokohama, Japan and Foundation of Physics Research Center (FoPRC), Cosenza, Italy.
*Author to whom correspondence should be addressed.
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.
Keywords: Wigner-Ville distribution, lehmer’s conjecture, ramanujan tau function, ramanujan’s zeta function, euler product