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The fractal dimension of the Riemann zeta zeros
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math.NT
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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.
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