The fractal dimension of the Riemann zeta zeros

Details The fractal dimension of the Riemann zeta zeros The fractal dimension of the Riemann zeta zeros

2011-02-18

arxiv.org/abs/1102.3764v1

Mathematics

Number Theory

6 pages, 1 figure

Scientific paper

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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