Artículos con la etiqueta ‘Hípotesis de Riemann’

A lattice gas of prime numbers and the Riemann Hypothesis

Por • 4 dic, 2012 • Category: Leyes

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.



On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function

Por • 24 mar, 2012 • Category: Educacion

The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Riemann zeta function is defined as a sum of the infinite number of items, in this paper, we look at the Riemann Hypothesis using a new applied approach to infinity allowing one to easily execute numerical computations with various infinite and infinitesimal numbers in accordance with the principle `The part is less than the whole’ observed in the physical world around us. The new approach allows one to work with functions and derivatives that can assume not only finite but also infinite and infinitesimal values and this possibility is used to study properties of the Riemann zeta function and the Dirichlet eta function. A new computational approach allowing one to evaluate these functions at certain points is proposed. Numerical examples are given. It is emphasized that different mathematical languages can be used to describe mathematical objects with different accuracies. The traditional and the new approaches are compared with respect to their application to the Riemann zeta function and the Dirichlet eta function. The accuracy of the obtained results is discussed in detail.



Physical interpretation of the Riemann hypothesis

Por • 19 feb, 2012 • Category: Educacion

An equivalent formulation of the Riemann hypothesis is given. The formulation is generalized. The physical interpretation of the Riemann hypothesis generalized formulation is given in the framework of quantum theory terminology. An axiom is laid down on the ground of the interpretation taking into account the observed properties of the surrounding reality. The Riemann hypothesis is true according to the axiom. It is shown that it is unprovable.