The fractal dimension of the Riemann zeta zeros

2011/02/18 by Jingbo Wang, Wang, Jingbo
Mathematics · #11m26 #11m50 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11m26 #msc:11m50

paper · pdf · doi:10.48550/arxiv.1102.3764

6 pages, 1 figure

arxiv created 2011/02/18 · arxiv updated 2011/02/21

Abstract

In this paper, we consider the nontrivial zeros of the Riemann zeta function as the eigenvalues of the Dirac operator on a fractal manifold. From the heat kernel expansion, we figure out that the fractal dimension of the manifold is about 1.1-1.2. Also we compare this result to the random matrix theory and the quantum chaos theory.

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