An Approach to PI(x) and other Arithmetical function by Variational principles

Details An Approach to PI(x) and other Arithmetical function by Variational principles An Approach to PI(x) and other Arithmetical function by Variational principles

2006-05-21

arxiv.org/abs/math/0605570v5

Mathematics

General Mathematics

This submission has been withdrawn by arXiv administrators because of fraudulently claimed institutional affiliation and statu

Scientific paper

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.

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