Number Theory

2106 Submissions

[9] viXra:2106.0143 [pdf] submitted on 2021-06-24 10:51:39

On the Density of Ulam Sequences

Authors: Theophilus Agama
Comments: 5 Pages.

In this paper we show under some special conditions that the natural density of Ulam numbers is zero.
Category: Number Theory

[8] viXra:2106.0120 [pdf] submitted on 2021-06-21 17:55:59

Notes on Critical Zeros of an L-function

Authors: Gorou Kaku
Comments: 43 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

This is the summary report of "Trace Formula in Noncommutative Geometry and the Zeros of the Riemman Zeta Function" by A.Connes.
Category: Number Theory

[7] viXra:2106.0076 [pdf] submitted on 2021-06-12 18:21:08

Riemann Hypothesis Proof Using Balazard, Saiasand Yor and Criterion

Authors: Shekhar Suman
Comments: 7 Pages. Please mail me your feedback [Corrections are made by viXra Admin to comply with the rules of viXra.org]

In this manuscript, we define a conformal map from the unit disc onto the semi plane. Later, we define a function f(z) = (s−1)ζ(s). We prove that f(z) belongs to the Hardy space,H1/3(D). We apply Jensen’s formula noting that the measure associated with the singularinterior factor of f is zero. Finally, we get∫∞−∞log|ζ(12+it)|14+t2dt=0.
Category: Number Theory

[6] viXra:2106.0052 [pdf] replaced on 2023-05-03 05:52:13

Particle Mass Ratios Nearly Equaling Geometric Ratios Additional Examples

Authors: Carl Littmann
Comments: 11 Pages.

There are many important Particle Mass Ratios in Physics, such as the 'Proton to electron' mass ratio, about 1836.15 to 1. And there are many major Volumetric ratios in 'Solid Geometry', some of which we may have seen in high school. And, remarkably, some of the major particle Mass ratios nearly equal some of those major geometric Volumetric ratios! This article gives many additional examples of these matches, which couldn't be included in my earlier article, but the earlier should be read first, preferably. Ref. http://viXra.org/abs/1901.0299 (But even both articles don't give all the important examples -- to avoid unwieldy length.)
Category: Number Theory

[5] viXra:2106.0050 [pdf] submitted on 2021-06-09 14:45:49

Twin Primes and Other Related Prime Generalization

Authors: Isaac Mor
Comments: 6 Pages.

I developed a very special summation function by using the floor function, which provides a characterization of twin primes and other related prime generalization.
Category: Number Theory

[4] viXra:2106.0029 [pdf] submitted on 2021-06-06 19:39:46

Plakkerige Viskeuze Ruimteoverdekking (Sticky Viscous Space Coverage)

Authors: J.A.J. van Leunen
Comments: 5 Pages. Dit is onderdeel van het Hilbert Book Model project

Ruimte kan worden bedekt met puntachtige objecten. Ruimte overdekt met een telbare verzameling puntachtige objecten gedraagt zich anders dan de ruimte die wordt bedekt door een ontelbare set puntachtige objecten.
Category: Number Theory

[3] viXra:2106.0028 [pdf] submitted on 2021-06-06 09:03:46

Sticky Viscous Space Coverage

Authors: J.A.J. van Leunen
Comments: 5 Pages. This is part of the Hilbert Book Model Project

Space can be covered with point-like objects. Space covered by a countable set of point-like objects behaves differently from space that is covered by an uncountable set of point-like objects.
Category: Number Theory

[2] viXra:2106.0015 [pdf] submitted on 2021-06-02 23:14:54

Pythagorean Common Prime Factor Conjecture

In this paper, the author proposes and proves a conjecture to be called the Pythagorean common prime factor conjecture, This conjecture states that if A^2 + B^2 = C^2, where A, B and C are positive integers, then A, B and C may have a common prime factor. The approach used in this paper is exactly the same as the approach used in proving the Beal conjecture (viXra:2012.0120 & viXra:2104.0098). To prove the Pythagorean common prime factor conjecture, one will let r, s and t be prime factors of A, B and C, respectively, such that A = Dr, B = Es, and C = Ft, where A, B and are positive integers. Then, the equation A^2 + B^2 = C^2, becomes (D^2)(r^2) + (E^2)(s^2) = (F^2)(t^2). The proof would be complete after proving that r^2 = t^2 and s^2 = t^2, which would imply that r = s = t. The proofs of the above equalities would also involve showing that the ratio, (r^2)/(t^2) =1 and the ratio (s^2)/(t^2) =1. Of the two numerical examples, 3^2 + 4^2 = 5^2 and 6^2 + 8^2 = 10^2, of the Pythagorean equation, the three terms of the first equation have no common prime factor; but the terms of the second equation have the common prime factor, 2. Perhaps, if there had been a Pythagorean common prime factor conjecture and its proof 24 years ago, Beal conjecture would have been proved 23 years ago. The main principle for obtaining relationships between the prime factors on the left side of the equation and the prime factor on the right side of the equation is that the power of each prime factor on the left side of the equation equals the same power of the prime factor on the right side of the equation. High school students can learn and prove this conjecture for a bonus question on a final class exam.
Category: Number Theory

[1] viXra:2106.0009 [pdf] submitted on 2021-06-03 14:06:08

Proofs of Three Conjectures in Number Theory : Beal's Conjecture, Riemann Hypothesis and The $ABC$ Conjecture

Authors: Abdelmajid Ben Hadj Salem
Comments: 106 Pages. The three proofs are under review. Comments welcome!

This monograph presents the proofs of 3 important conjectures in the field of Number theory: - The Beal's conjecture. - The Riemann Hypothesis. - The $abc$ conjecture. We give in detail all the proofs.
Category: Number Theory