Open AccessWigner Distribution Analysis Applied to Lehmer’s Conjecture on the Ramanujan tau Function
Author(s) -
Takaaki Musha
Publication year - 2021
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2021/v17i730315
Subject(s) - ramanujan's sum , mathematics , wigner distribution function , ramanujan tau function , distribution (mathematics) , dirichlet distribution , euler's formula , dirichlet series , conjecture , series (stratigraphy) , pure mathematics , mathematical analysis , physics , quantum mechanics , quantum , boundary value problem , paleontology , biology
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.