Number Theory

1010 Submissions

[8] viXra:1010.0064 [pdf] submitted on 31 Oct 2010

The New Prime Theorems (791)-(840)

Authors: Chun-Xuan Jiang
Comments: 71 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 (791)-(840) contain infinitely many prime solutions and no prime solutions. From (6) we are able to find the smallest solution πk(N0,2) ≥ 1. This is the Book theorem.
Category: Number Theory

[7] viXra:1010.0049 [pdf] submitted on 20 Mar 2010

Open Questions About Concatenated Primes and Metasequences

Authors: Florentin Smarandache
Comments: 3 pages

We define a metasequence as a sequence constructed with the terms of other given sequence(s). In this short note we present some open questions on concatenated primes involved in metasequences.
Category: Number Theory

[6] viXra:1010.0048 [pdf] submitted on 20 Mar 2010

Generalization and Alternatives of Kaprekar's Routine

Authors: Florentin Smarandache
Comments: 5 pages

We extend Kaprekar's Routine for a large class of applications. We also give particular examples of this generalization as alternatives to Kaprekar's Routine and Number. Some open questions about the length of the iterations until reaching either zero or a constant or a cycle, and about the length of the cycles are asked at the end.
Category: Number Theory

[5] viXra:1010.0043 [pdf] submitted on 26 Oct 2010

Bhaskaracharya Quadratics and Spade Sequences

Authors: Nathaniel S. K. Hellerstein
Comments: 13 pages

In this article I generalize on a word problem by Bhaskaracharya. The resulting quadratics are trivial to solve; but composing them, so that they have whole number solutions, is not trivial. In this article I discover a class of sequences, which I call "Spade Sequences" as homage to a hero of detective fiction, which generate both Bhaskaracharya quadratics and their solutions. The article ends with a list of such word problems, presented as a problem set with answer key.
Category: Number Theory

[4] viXra:1010.0019 [pdf] submitted on 9 Oct 2010

Research on Number Theory and Smarandache Notions

Authors: Z. Wenpeng
Comments: 151 pages

This Book is devoted to the proceedings of the Sixth International Conference on Number Theory and Smarandache Notions held in Tianshui during April 24-25, 2010. The organizers were myself and Professor Wangsheng He from Tianshui Normal University. The conference was supported by Tianshui Normal University and there were more than 100 participants. We had one foreign guest, Professor K.Chakraborty from India. The conference was a great success and will give a strong impact on the development of number theory in general and Smarandache Notions in particular. We hope this will become a tradition in our country and will continue to grow. And indeed we are planning to organize the seventh conference in coming March which will be held in Weinan, a beautiful city of shaanxi.
Category: Number Theory

[3] viXra:1010.0017 [pdf] replaced on 16 Dec 2010

Resolution of Riemann Hypothesis

Authors: Pankaj Mani
Comments: 5 pages

The Riemann hypothesis is proved to be true which states that all the non-trivial zeros of Riemann zeta function lie along the line R(z)=1/2 for 0<R(z)<1. The work done here clarifies that there is no need to find out the non-trivial zeros of the Riemann zeta function to prove the Riemann hypothesis true as the Riemann hypothesis must be true for the functional equation satisfied by the zeta function to exist itself structurally in mathematics.
Category: Number Theory

[2] viXra:1010.0006 [pdf] replaced on 17 Oct 2010

Power Structures in Finite Fields and the Riemann Hypothesis

Authors: Alessandro Dallari
Comments: 46 pages

Some tools are discussed, in order to build power structures of primitive roots in finite fields for any order qk; relations between distinct roots are deduced from m- and shift-and-add- sequences. Some heuristic computational techniques, where information in a m- sequence is built from below, are proposed. Full settlement is finally viewed in a physical scenario, where a path leading to the Riemann Hypothesis can be enlighted.
Category: Number Theory

[1] viXra:1010.0004 [pdf] submitted on 1 Oct 2010

The New Prime Theorem (741)-(790)

Authors: Chun-Xuan Jiang
Comments: 71 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 (741)-(790) contain infinitely many prime solutions and no prime solutions. From (6) we are able to find the smallest solution πk(N0,2) ≥ 1. This is the Book theorem.
Category: Number Theory