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On the evaluation of certain arithmetical functions of number theory and their sums and a generalization of riemann-weil formula

Author:

Moreta, Jose Javier Garcia

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

November 5, 2024

File:

/Research Papers-Mathematics and Applied Mathematics/Download/9990

Downloads:

Keywords:

PNT (prime number theorem), Variational Calculus, Maxima and minima, Integral Transforms.

Abstract:

In this paper we present a method to get the prime counting function π(x) and other arithmetical functions than can be generated by a Dirichlet series, first we use the general variational method to derive the solution for a Fredholm Integral equation of first kind with symmetric Kernel K(x,y)=K(y,x), after that we find another integral equations with Kernels K(s,t)=K(t,s) for the Prime counting function

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