The fractal dimension of the Riemann zeta zeros

Jingbo Wang

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The fractal dimension of the Riemann zeta zeros

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arxiv 1102.3764 v1 pith:TRIPP25U submitted 2011-02-18 math.NT

The fractal dimension of the Riemann zeta zeros

Jingbo Wang This is my paper

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keywords fractaldimensionmanifoldriemanntheoryzeroszetachaos

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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.

The fractal dimension of the Riemann zeta zeros

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