Explicit formula and quasicrystal definition

2024/02/16 by de Reyna, J. Arias
#11M26 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.10604

Abstract

We show that the Riemann hypothesis is true if and only if the measure μ=-∑_n=1^∞(Λ(n))/(√(n))(δ_{log n}+δ_{-log n})+2\cosh(x/2) dx is a tempered distribution. In this case it is the Fourier transform of another measure F(∑_γδ_γ/2π-2ϑ'(2πt) dt)=μ. We propose a definition of Fourier quasi-crystal to make sense of Dyson suggestion.

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