Acerca de un Problema Elemental Equivalente a la Hipótesis de Riemann

Abstract

One of the most important, interesting and difficult problems in Mathematics has been to obtain a succession that can produce prime numbers, the greatest advance in the solution of this problem was obtained when Bernhard Riemann from his studies on the Prime-counting function and the zeta function, formulated what is now known as the Riemann hypothesis. In this paper a study is made on the E problem equivalent to the Riemann hypothesis proposed by Jeffrey Lagarias, starting with the study of how the zeta function was born from an idea of Euler, and how Riemann manages to define it in All the complex plane thus arriving at the formulation of its famous hypothesis, after this the problem of the relative error for the theorem of prime numbers is shown that turns out to be equivalent to the hypothesis, followed by a study of the ideas that led to Lagarias In the formulation of his problem, culminating with the demonstration that to solve the E problem is equivalent to give solution to the Hypothesis of Riemann. Thus this paper turns out to be an analysis of the evolution and implications that the Riemman hypothesis has had, starting from its origin and ending in the Lagarias E problem.