Number Theory

1203 Submissions

[6] viXra:1203.0075 [pdf] submitted on 2012-03-19 10:44:15

Note on Quadratic Residues For Primes of the Form 4K+3Louis

Authors: Louis D. Grey
Comments: 3 Pages.

It is a well known result that for a prime of the form 4k+3, there are more quadratic residues than non-residues in the interval (1,(p-1)/2). Using elementary methods,we provide an asymptotic estimate for the number of residues in the interval.
Category: Number Theory

[5] viXra:1203.0073 [pdf] submitted on 2012-03-19 11:47:19

Note On Quadratic Residues For Primes of The Form 4k+3

Authors: Louis D. Grey
Comments: Pages. Remove word "louis" after title of paper

We prove a special case of C.L. Siegel's theorem regarding the class number of binary quadratic forms with fundamental discriminant -D<0.
Category: Number Theory

[4] viXra:1203.0064 [pdf] replaced on 2017-09-10 09:26:00

The Goldbach Conjecture

Authors: Ricardo G. Barca
Comments: 43 Pages. Extended explanation in the Introduction.

The binary Goldbach conjecture asserts that every even integer greater than 4 is the sum of two primes. In order to prove this statement, we start by defining a kind of double sieve of Eratosthenes as follows. Given an even integer x, we sift out from [1, x] all those elements that are congruents to 0 modulo p, or congruents to x modulo p, where p is a prime less than the square root of x. So, any integer in the interval [sqrt{x}, x] that remains unsifted is a prime p for which either x-p = 1 or x-p is also a prime. Then, we introduce a new way to formulate this sieve, which we call the sequence of k-tuples of remainders. Using this tool, we obtain a lower bound for the number of elements in [1, x] that survives the sifting process. We prove, for every even number x greater than the square of 149, that there exist at least 3 integers in the interval [ 1, x ] that remains unsifted. This proves the binary Goldbach conjecture for every even number x greater than the square of 149, which is our main result.
Category: Number Theory

[3] viXra:1203.0060 [pdf] submitted on 2012-03-16 02:45:52

The New Prime Theorems(1441)-(1490)

Authors: Chun-Xuan Jiang
Comments: 90 Pages. It is the very important paper for number theory

Using Jiang function we prove the new prime theorems(1441)-(1480).
Category: Number Theory

[2] viXra:1203.0050 [pdf] submitted on 2012-03-14 19:21:00

The New Prime Theorems(1491)-(1540)

Authors: Chun-Xuan Jiang
Comments: 90 Pages.

using Jiang function we prove the new prime theorems(1491)-��1540��
Category: Number Theory

[1] viXra:1203.0019 [pdf] replaced on 2012-03-06 19:53:44

Riemann Hypothesis and Conjecture of Birch and Swinnerton-Dyer Are False

Authors: Chun-Xuan Jiang
Comments: 5 Pages.

All eyes are on the Riemann hypothesis,zeta and L-functions ,which are false ,please read this paper.
Category: Number Theory