Phase space distribution of Riemann zeros

Distribution of the zeros of the Riemann Zeta function

One of the most celebrated problem of mathematics is the Riemann hypothesis which states that all the non trivial zeros of the Zeta-function lie on the critical line <(s) = 1/2. Even if this famous problem is unsolved for so long, a lot of things are known about the zeros of ζ(s) and we expose here the most classical related results : all the non trivial zeros lie in the critical strip, the num...

Landau levels and Riemann zeros.

The number N(E) of complex zeros of the Riemann zeta function with positive imaginary part less than E is the sum of a "smooth" function N[over ](E) and a "fluctuation." Berry and Keating have shown that the asymptotic expansion of N[over ](E) counts states of positive energy less than E in a "regularized" semiclassical model with classical Hamiltonian H=xp. For a different regularization, Conn...

A Study of the Riemann Zeta Zeros

The goals of the proposed research are: 1) To obtain additional concrete computational evidence §2.1 of the unknown structure on the imaginary parts of the non-trivial zeros of the Riemann zeta function, called herein the Riemann spectrum, following the method from [1]; specifically, the PI will compute correlations between histograms of random variables Xp (§2); 2) To prove the that the densit...

Simple Zeros of the Riemann Zeta-function

Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25% of the zeros of the Riemann zeta-function are simple. Using Montgomery and Taylor's argument together with an elementary combinatorial argument, we prove that assuming the Riemann Hypothesis at least 67.275% of the zeros are simple.

Correlations of Eigenvalues and Riemann Zeros