Number Theory

1001 Submissions

[4] viXra:1001.0047 [pdf] submitted on 29 Jan 2010

An Approach to π(x) and Other Arithmetical Functions by Variational Principles

Authors: Jose Javier Garcia Moreta
Comments: 11 Pages.

In this paper we present a method to get the prime counting function p(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 and other arithmetical functions generated by Dirichlet series, then we could find a solution for ... (see paper for full abstract)
Category: Number Theory

[3] viXra:1001.0042 [pdf] replaced on 28 Jun 2010

Zeta Regularization Applied to the Problem of Riemann Hypothesis and the Calculation of Divergent Integrals

Authors: Jose Javier Garcia Moreta
Comments: 18 Pages.

In this paper we review some results of our previous papers involving Riemann Hypothesis in the sense of Operator theory (Hilbert-Polya approach) and the application of the negative values of the Zeta function ... (see paper for full abstract)
Category: Number Theory

[2] viXra:1001.0039 [pdf] submitted on 26 Jan 2010

A Comment on Mathematical Methods to Deal with Divergent Series and Integrals

Authors: Jose Javier Garcia Moreta
Comments: 14 Pages.

In this paper we study the methods of Borel and Nachbin resummation applied to the solution of integral equation with Kernels K(yx) , the resummation of divergent series and the possible application to Hadamard finite-part integral and distribution theory.
Category: Number Theory

[1] viXra:1001.0038 [pdf] replaced on 7 Mar 2010

A Note on the Mellin Convolution of Functions and Its Relation to Riesz Criterion and Riemann Hypothesis

Authors: Jose Javier Garcia Moreta
Comments: 8 Pages.

In this paper we study how the Mellin convolution of functions f and g ( f * g ) and how is related to the Riesz criterion for the Riemann Hypothesis, the idea is to stablish a Fredholm integral equation of First kind for the Riesz function and the Hardy function.
Category: Number Theory