Tuesday, May 10, 2011

A Dynamical Key to the Riemann Hypothesis

Riemann zeta function and a series of Dirichlet L-functions
followed by a naked non-L function with zeros off the critical line.

I've just completed a new dynamic paper on the Riemann Hypothesis with movies.
A Dynamical Key to the Riemann Hypothesis
using a new generation of my Mac RZViewer application, which now portrays diverse L-functions and makes dynamic movies of the zeros varying as the functions are transformed:
Riemann Zeta Function Viewer 1.5 Flight Manual

The new paper sets out a dynamical basis for the non-trivial zeros of the Riemann zeta function being on the critical line x = 1/2. It provides an explanation for why zeta and the Dirichlet L-functions do have their non-trivial zeros on the critical line and why other closely related functions do not. It suggests RH is an additional unprovable postulate of the number system, similar to the axiom of choice, associated with the limiting behavior of the primes as tends to infinity.