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| viXra.org > Number Theory > 2303 |
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[10] viXra:2303.0165 [pdf] submitted on 2023-03-31 01:19:13
Authors: Ryan J. Buchanan
Comments: 4 Pages.
Succession is placed ie orderings are consideredmber rings. Linear-style orderings are considered as operads which split fields by introducing locally transcendental numbers that perfectly close their ancestors by introducing gaps.
Category: Number Theory
[9] viXra:2303.0153 [pdf] submitted on 2023-03-27 03:44:02
Authors: Huhnkie Lee
Comments: 36 Pages.
Probabilistic Proof of Goldbach's Conjecture is presented. Philosophical, political, and historical narratives tangentially related to Goldbach’s Conjecture are provided.
Category: Number Theory
[8] viXra:2303.0121 [pdf] submitted on 2023-03-21 01:02:40
Authors: Gennady Butov
Comments: 20 Pages.
Two hypotheses are put forward about the infinity of intersecting ellipses and hyperbolas, which are given in the form of equations with prime numbers.1. Representation of the sum of two prime numbers in the form of an ellipse equation.Determining the conditions for the intersection of hyperbolas when decomposing even numbers into two primes.2. Representing the difference of two prime numbers as a hyperbolic equation.Determining the conditions for the intersection of ellipses in the decomposition of even numbers into two primes.
Category: Number Theory
[7] viXra:2303.0102 [pdf] replaced on 2025-01-18 14:37:33
Authors: Abdelmajid Ben Hadj Salem
Comments: 8 Pages. Submitted to one journal of the London Mathematical Society.
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann Hypothesis : The nontrivial roots (zeros) $s=sigma+it$ of the zeta function, defined by: $$zeta(s) = sum_{n=1}^{+infty}frac{1}{n^s},,mbox{for}quad Re(s)>1$$ have real part} $sigma= frac{1}{2}$. In this note, I will give the proof that $sigma=1/2$ using an equivalent statement of the Riemann Hypothesis concerning the Dirichlet $eta$ function.
Category: Number Theory
[6] viXra:2303.0091 [pdf] replaced on 2023-03-28 00:33:24
Authors: Durmagambetov Asset, Durmagambetov Aniyar
Comments: 6 Pages.
The paper analyzes the number of zeros in the binary representation of a natural number. The analysis is carried out using the concept of the fractional part of a number, which naturally arises when finding a binary representation. This idea relies on the fundamental property of the Riemann zeta function, which is constructed using the fractional part of a number. Understanding that the ratio of the fractional and integer parts, by analogy with the Riemann zeta function, expresses the deep laws of numbers, will explain the essence of this work. For the Syracuse sequence of numbers that appears in the Collatz conjecture, we use a binary representation that allows us to obtain a uniform estimate for all terms of the series, and this estimate depends only on the initial term of the Syracuse sequence. This estimate immediately leads to the solution of the Collatz conjecture
Category: Number Theory
[5] viXra:2303.0067 [pdf] submitted on 2023-03-10 02:18:15
Authors: Justin Walter
Comments: 1 Page.
This short paper is about the non-trivial zeros of Riemann Hypothesis.
Category: Number Theory
[4] viXra:2303.0065 [pdf] submitted on 2023-03-09 10:42:03
Authors: Marko V. Jankovic
Comments: 11 Pages.
In this paper it is going to be proved that exists infinitely many primes that are of the form n^2+1.
Category: Number Theory
[3] viXra:2303.0029 [pdf] submitted on 2023-03-04 10:27:30
Authors: Giovanni Di Savino
Comments: 41 Pages.
All prime numbers, less than the result of powers of prime numbers ≥2^n, generate perfect numbers; the prime numbers which, from the result of 2^n, are an odd number ≥1 away generate the even perfect numbers which are the result of: ((2^n -1)* 2^(n-1))/(2- 1); the prime numbers which, from the result of powers of prime numbers ≥3^n, are distant by an even number ≥2 generate the perfect odd numbers which are the result of: ((prime≥3 -2)*prime ≥3^(n- 1) )/(first ≥3 -1).
Category: Number Theory
[2] viXra:2303.0021 [pdf] submitted on 2023-03-05 16:36:00
Authors: Edgar Valdebenito
Comments: 3 Pages.
Via symbolic summation method, we establish many series for pi^2 .
Category: Number Theory
[1] viXra:2303.0020 [pdf] submitted on 2023-03-05 17:01:26
Authors: Miguel Cerdá Bennassar
Comments: 6 Pages.
In this paper I present a study of the Collatz problem and its conjecture using graph theory and the properties of the digital root of natural numbers.
Category: Number Theory
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