Number Theory

1012 Submissions

[13] viXra:1012.0047 [pdf] submitted on 23 Dec 2010

The New Prime Theorems (841)-(890)

Authors: Chun-Xuan Jiang
Comments: 95 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 J2(ω) we prove that the new prime theorems (841)-(890) contain infinitely many prime solutions and no prime solutions. From (6) we are able to find the smallest solution (see paper). This is the Book theorem.
Category: Number Theory

[12] viXra:1012.0036 [pdf] submitted on 15 Dec 2010

A Treaty of Symmetric Function Part V Using Sum of Power for Arbitrary Arithmetic Progression for Studies of Prime Numbers that Coexist Within the Equation Formed Through a New Conjecture of Symmetric Function Rule of Division

Authors: Mohd Shukri Abd Shukor
Comments: 30 pages

A new approach in deriving Sum of Power series using reverse look up method, a method where a mathematical formulation is constructed from set of data. Faulhaber [1] derived a general equation for Power sums and calculated the terms up to (Part V)
Category: Number Theory

[11] viXra:1012.0035 [pdf] submitted on 15 Dec 2010

A Treaty of Symmetric Function Part IV Using Sums of Power for Arbitrary Arithmetic Progression to Find an Approximation for Sum of Power for Non-Integers R-th Power and Expressing Riemann's Zeta Function Into Symmetric Sums of Power Form.

Authors: Mohd Shukri Abd Shukor
Comments: 19 pages

A new approach in deriving Sum of Power series using reverse look up method, a ,method where a mathematical formulation is constructed from set of data. Faulhaber [1] derived a general equation for Power sums and calculated the terms up to (Part IV)
Category: Number Theory

[10] viXra:1012.0034 [pdf] submitted on 15 Dec 2010

A Treaty of Symmetric Function Part III an Approach in Deriving General Formulation for Alternating Sums of Power for an Arbitrary Arithmetic Progression.

Authors: Mohd Shukri Abd Shukor
Comments: 19 pages

An extension of Sum of Power formulation into alternating system. The general formulation is given as follows:
Category: Number Theory

[9] viXra:1012.0033 [pdf] submitted on 15 Dec 2010

A Treaty of Symmetric Function Part II Sums of Power for an Arbitrary Arithmetic Progression for Real Power-P

Authors: Mohd Shukri Abd Shukor
Comments: 18 pages

Sums of Power mainly deal with positive integer power p (i.e. p ε+ Z). In this paper, I would like to show that the sums of power that I had formulated in paper part I [1] also can be applied to the non-integer power p. The sums of power for positive non-integers (i.e. SPPNI) in this paper still adopting the same general sums of power formulation. However, the value of m has no bound and it is used as precision control. The larger the value of m used, the more accuracy the result would be.
Category: Number Theory

[8] viXra:1012.0032 [pdf] replaced on 19 Nov 2011

A Treaty of Symmetric Function Part 1 Sums of Power

Authors: Mohd Shukri Abd Shukor
Comments: 47 pages

Sum of Power had gathered interest of many classical mathematicians for more than two thousand years ago. The quests of finding sum of power or discrete sum of numerical power can be traced back from the time of Archimedes in third BC then to Faulhaber in the sixteen century. Until today there is no closed form sums of power formulation for an arithmetic progression has been found. Many mathematicians were involved in this research and many approaches have been introduced but none is found to be conclusive. The generalized equation for sums of power discovered in this research has been compared to Faulhaber's sums of power for integers and it is found that this new generalized equation can be used for both integers and arithmetic progression, thus offering a new frontier in studying symmetric function, Fermat's last theorem, Riemman's Zeta function etc.
Category: Number Theory

[7] viXra:1012.0022 [pdf] replaced on 9 Jan 2011

Automorphic Function And Fermat's Last Theorem (6)

Authors: Chun-Xuan Jiang
Comments: 24 pages

In 1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (part 6)
Category: Number Theory

[6] viXra:1012.0021 [pdf] replaced on 9 Jan 2011

Automorphic Function And Fermat's Last Theorem (5)

Authors: Chun-Xuan Jiang
Comments: 25 pages

In 1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (part 5)
Category: Number Theory

[5] viXra:1012.0010 [pdf] replaced on 9 Jan 2011

Aotomorphic Functions And Fermat's Last Theorem (4)

Authors: Chun-Xuan Jiang
Comments: 27 pages

In 1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (part 4)
Category: Number Theory

[4] viXra:1012.0009 [pdf] replaced on 9 Jan 2011

Automorphic Function And Fermat's Last Theorem (3) (Fermat's Proof of FLT)

Authors: Chun-Xuan Jiang
Comments: 25 pages

In 1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (part 3)
Category: Number Theory

[3] viXra:1012.0008 [pdf] replaced on 9 Jan 2011

Automorphic Function And Fermat's Last Theorem(2)

Authors: Chun-Xuan Jiang
Comments: 25 pages

In 1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (part 2)
Category: Number Theory

[2] viXra:1012.0007 [pdf] replaced on 12 Jan 2011

Automorphic Functions And Fermat's Last Theorem(1)

Authors: Chun-Xuan Jiang
Comments: 27 pages

In 1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (part 1)
Category: Number Theory

[1] viXra:1012.0004 [pdf] submitted on 2 Dec 2010

Goldbach' Conjecture (10): The Six Details in the Hardy-Littlewood Conjecture (A)

Authors: Tong Xin Ping
Comments: 6 pages, in Chinese

This paper is to discuss the six details in the Hardy-Littlewood Conjecture (A):...
Category: Number Theory