1211.6621 (Fernando Vericat)

A lattice gas of prime numbers and the Riemann Hypothesis    [PDF]

Fernando Vericat

In recent years there has been some interest in applying ideas and methods taken from Physics in order to approach several challenging mathematical problems, particularly the Riemann Hypothesis, perhaps motived by the apparent inaccessibility to their solution from a full rigorous mathematical point of view. Most of these kind of contributions are suggested by some quantum statistical physics problems or by questions originated in chaos theory. In this note, starting from a very simple model of one-dimensional lattice gas and using the concept of equilibrium states as being described by Gibbs measures, we link classical statistical mechanics to the Riemann Hypothesis.

View original: http://arxiv.org/abs/1211.6621