Number Theory

1110 Submissions

[5] viXra:1110.0054 [pdf] submitted on 18 Oct 2011

Gauge Transformations and the Riemann Hypothesis

Authors: Thomas Evans
Comments: 9 pages

Presented is a new determination of conditions proving the Riemann Hypothesis of any global L-function, drawing heavily on conceptual and mathematical parallels from quantum theory, specifically those summarized by Bohm in his 1951 text. We present a proof of this for a special case concerning the function ζ(s) , defined by Riemann in his seminal 1859 paper, "On the number of primes less than a given number". A new method of defining a system of inverted concatenations at the simple pole(s) of a global L-function is introduced and used to finalize our proof.
Category: Number Theory

[4] viXra:1110.0051 [pdf] replaced on 4 Nov 2011

The New Prime Theorems (1141)-(1190)

Authors: Chun-Xuan Jiang
Comments: 90 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. No great mathematicians study prime problems and prove Riemann hypothesis in AIM, CLAYMI, IAS, THES, MPIM, MSRI. In this paper using Jiang function we prove that the new prime theorems (1141)-(1190) contain infinitely many prime solutions and no prime solutions. From (6) we are able to find the smallest solution. This is the Book theorem.
Category: Number Theory

[3] viXra:1110.0045 [pdf] submitted on 14 Oct 2011

Relationship Between Irrational Constants Phi and e (Including New Equations, Possible Implications)

Authors: Prateek Goel
Comments: 6 pages.

Relationship between irrational constants Phi and e (including new equations, possible implications)
Category: Number Theory

[2] viXra:1110.0041 [pdf] submitted on 13 Oct 2011

On the Sums (See Paper) and Their Relation to the Riemann Hypothesis and the Riemannweil Formula

Authors: Jose Javier Garcia Moreta
Comments: 7 pages

We study the sums (see paper) evaluated over the zeros and the imaginary part of the zeros of the Riemann Zeta function by two methods, the first method involves the use of the Hadamard product formula for the Riemann Xi-function, the second one uses the Riemann-Weill explicit formula , which relates a sum over the imaginary part of the zeros with another sum over prime numbers , we have managed to prove that the sum (see paper)
Category: Number Theory

[1] viXra:1110.0032 [pdf] replaced on 3 Nov 2011

The New Prime Theorems (1091)-(1140)

Authors: Chun-Xuan Jiang
Comments: 90 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. No great mathematicians study prime problems and prove Riemann hypothesis in AIM, CLAYMI, IAS, THES, MPIM, MSRI. In this paper using Jiang function we prove that the new prime theorems (1091)-(1140) contain infinitely many prime solutions and no prime solutions. From (6) we are able to find the smallest solution. This is the Book theorem.
Category: Number Theory