The fractal dimension of the Riemann zeta zeros

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.

6 pages, 1 figure

References in corpus (1)

• H = x p with interaction and the Riemann zeros