  In this paper we present a method to derive Pi(x) and other Arithemtical
functions that can be generated by a Dirichlet series by variational
principles,we use a variational method to determine the solution for a Fredholm
integral equation of second kind, after that we propose (obtain) two integral
equations one for the Pi(x) and other for the arithmetical function
A(x)=Sum(n,x)a(n) so they can be solved by usual optimization method. Also some
conjectures on the value for the asymptotic value of the sum of f(t)=t^{n} are
given in the form Li(x^{n+1})
  Changes: Rayleigh-ritz Variational Methods added, we have also included a
brief description of how to accelerate the convergence of the series
Sum{p}f(x),Grammar changes.
