# Number Theory

## 1205 Submissions

 viXra:1205.0118 [pdf] replaced on 2013-05-24 10:38:39

### The Goldbach Conjecture - Solutions

Authors: Bertrand Wong

The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003 and had since then been working on the solutions for the Goldbach conjecture, which is another problem relating to the prime numbers. This paper, which comprises of 4 parts that are each self-contained, is a combination and modification of the author’s 2 papers published recently in another international mathematics journal. The expected mode of solving the Goldbach conjecture appears to be the utilisation of advanced calculus or analysis, e.g., by the summation, or, integration, of the reciprocals involving directly or indirectly the primes to see whether they converge or diverge, in order to get a “feel” of the pattern of the distribution of the primes. But, such a method of solving the problem has evidently not succeeded so far. Some other approach or approaches could be more appropriate. This paper brings up a number of such approaches.
Category: Number Theory

 viXra:1205.0108 [pdf] submitted on 2012-05-29 23:56:06

### Some Issues on Goldbach Conjecture

Authors: Emmanuel Markakis, Christopher Provatidis, Nikiforos Markakis

This paper presents a deterministic process of finding all pairs (p,q) of odd numbers (composites and primes) of natural numbers ≥ 3 whose sum (p + q) is equal to a given even natural number 2n ≥ 6. Subsequently, based on the above procedure and also relying on the distribution of primes in the set of natural numbers, we propose a closed analytical formula, which estimates the number of primes which satisfy Goldbach’s conjecture for positive integers ≥ 6.
Category: Number Theory

 viXra:1205.0099 [pdf] submitted on 2012-05-25 06:49:29

### The Fundamental Proof of the Number Theory

Authors: Maik Becker-Sievert

(n+a)= 2n+(a-n)=2n-(n-a) proofs direct Goldbach Conjecture , 1 is prime Levys = Lemoine's Conjecture with a,n are primes Polignacs Conjecture
Category: Number Theory

 viXra:1205.0077 [pdf] submitted on 2012-05-19 16:01:41

### (This Paper Has Been Withdrawn by the Author)

Authors: Germán Paz
Comments: 44 Pages. Withdrawn.

This paper has been withdrawn by the author due to a flaw in the proof. / Este documento ha sido retirado por el autor debido a un error en la demostración.
Category: Number Theory

 viXra:1205.0076 [pdf] replaced on 2012-06-23 13:52:48

### A Finite Reflection Formula For A Polynomial Approximation To The Riemann Zeta Function

Authors: Stephen Crowley

The Riemann zeta function can be written as the Mellin transform of the unit interval map w(x)=⌊x−1⌋(x⌊x−1⌋+x−1) multiplied by s((s+1)/(s-1)). A finite-sum approximation to ζ(s) denoted by ζw(N;s) which has real roots at s=−1 and s=0 is examined and an associated function χ(N;s) is found which solves the reflection formula ζw(N;1−s)=χ(N;s)ζw(N;s). A closed-form expression for the integral of ζw(N;s) over the interval s=-1..0 is given. The function χ(N;s) is singular at s=0 and the residue at this point changes sign from negative to positive between the values of N = 176 and N = 177. Some rather elegant graphs of ζw(N;s) and the reflection functions χ(N;s) are also provided. The values ζw(N;1−n) for integer values of n are found to be related to the Bernoulli numbers.
Category: Number Theory

 viXra:1205.0042 [pdf] submitted on 2012-05-07 20:38:15

### The New Prime Theorems(1541)-(1590)

Authors: Chun-Xuan Jiang