| viXra.org > Number Theory > 2201 |
 |
 |
| viXra.org > Number Theory > 2201 |
|
|
[12] viXra:2201.0216 [pdf] submitted on 2022-01-31 20:28:09
Authors: Edoardo Gueglio
Comments: 5 Pages.
It is possible to define a chain of recurrence relations starting from partition function
involving another partition function whose parameters vary along with the recurrence
relations.
Category: Number Theory
[11] viXra:2201.0215 [pdf] replaced on 2024-06-30 03:26:49
Authors: Lei Shi
Comments: 27 Pages.
It is proved that· For any positive integer d, there are infinitely many prime gaps of size 2d.· Every even number greater than 2 is the sum of two prime numbers.Our method from the analysis of distribution density of pseudo primes in specific set is to transform them into upper bound problem of the maximum gaps between overlapping pseudo primes, then the two are essentially the same problem.
Category: Number Theory
[10] viXra:2201.0213 [pdf] submitted on 2022-01-30 18:07:07
Authors: Sudarshan Saha
Comments: 22 Pages.
If $m$ divides $n$ then $\sin(n\pi/m) = 0$. By counting number of zeros of $\sin(n\pi/m)$ for a given $n \in \mathds{Z}$ and $m \in \mathds{Z}$, we can find the total number of divisors that $n$ has and in this way, we can construct a series representation of the \emph{Number-of-divisors function}, $\mathcal{S}(n)$. Similarly, we can find a closed-form of another important integer-valued function in Number Theory, \emph{Sum-of-divisors function}, $\sigma(n)$. After constructing series representation of these functions we can resolve a well-known conjecture in Number Theory -- the \emph{Riemann Conjecture}. To conclude the Riemann conjecture we use \emph{Robin's inequality} which sets an upper limit of $\sigma(n)$ for $n>5040$, if Riemann conjecture is true. This method can be trivially extended to the other higher-order divisor functions. To construct these series representations we have explored \emph{Matsubara} technique which is commonly used in Condensed Matter Physics to perform various sums over integer index with a contour integral.
Category: Number Theory
[9] viXra:2201.0194 [pdf] submitted on 2022-01-27 11:54:20
Authors: Denis Gallet
Comments: 9 Pages.
In this paper,I study values of Barnes G function as G(k/8) and G(k/12) with Wallis product as applications.And I write several formulas, so we can evaluate elementary values.
Category: Number Theory
[8] viXra:2201.0151 [pdf] replaced on 2023-07-13 12:18:16
Authors: Kouji Takaki
Comments: 3 Pages.
We showed that Firoozbakht's conjecture holds when p_(n+1)-p_n≧log(p_n) holds.
Category: Number Theory
[7] viXra:2201.0149 [pdf] submitted on 2022-01-23 18:56:54
Authors: Marc Schofield
Comments: 14 Pages. [Corrections made by viXra Admin to conform with scholarly norm]
Tetrahedral numbers have a well-defined construction but are not the only way of building tetrahedra from numbers, as is evidenced in studies we will briefly consider as a motivation for looking at the following proposed construction of number shapes, this being a new perspective on a pattern often written in a slightly different context, to a different stacking of numbers. We will go on to look at a few properties of shapes built from this novel construction, including a few specific shapes built from prime numbers, taking us neatly into some parabolic equations with prime-heavy cartesian coordinates.
Category: Number Theory
[6] viXra:2201.0096 [pdf] submitted on 2022-01-16 14:19:05
Authors: Federico Gabriel
Comments: 1 Page.
In this article a conjecture about nonlinear relation between primes is proposed.
Category: Number Theory
[5] viXra:2201.0067 [pdf] replaced on 2025-09-13 22:51:29
Authors: Zhang Tianshu
Comments: 18 Pages.
The subject of this article is exactly to analyze Beal’s conjecture and prove it. This proof involves certain basic knowledge of algebra, number theory, and the symmetry of odd points on the number axis. First, we classify mathematical expressions which consist of AX, BY and CZ according to the parity of A, B and C, so get rid of two combinations of AX, BY and CZ, for they have nothing to do with the conjecture. For the remaining two cases, we first prove the equation AX+BY=CZ by examples where A, B, and C have at least one common prime factor. Then prove each kind of AX+BY≠CZ by arithmetic fundamental theorem, the mathematical induction, the binomial theorem, the reduction to absurdity, and the interrelation between a sum of two odd numbers and an even number that served as the center of symmetry, where A, B, and C have not a common prime factor, and that each proof takes what it needs.
Category: Number Theory
[4] viXra:2201.0065 [pdf] submitted on 2022-01-11 08:10:14
Authors: Edgar Valdebenito
Comments: 2 Pages.
We give an integral involving the Gamma function and the Lambert W-function.
Category: Number Theory
[3] viXra:2201.0062 [pdf] submitted on 2022-01-11 13:09:37
Authors: Arthur Shevenyonov
Comments: 8 Pages. a single-line RH proof accrues just naturally
The paper proposes an elegant generalization straddling beyond arithmetic series summation and functional integration/analysis alike. Based on computationally efficient averaging without necessarily invoking any classic criteria/filters/cut-offs, notably continuity or convergence checks, it leads just naturally up to applications to RH (boasting a single-line demonstration). Extra implications for primes and, more broadly, numbers-theoretic pursuits as well as functional operators will be forthcoming as part of a full-fledged roundup, with a summary glimpse allowed herewith.
Category: Number Theory
[2] viXra:2201.0048 [pdf] submitted on 2022-01-09 18:33:24
Authors: J. W. L. Eerland
Comments: 24 Pages.
The cannonball problem asks which numbers are both square and square pyramidal. In this paper I consider the cannonball problem for other $r$-regular polygons. I carried out a computer search and found a total of $858$ solutions for polygons $3\le r\le10^5$. By using elliptic curves I also found that there are no solutions for $r=5$ (pentagon), $r=7$ (heptagon), and $r=9$ (enneagon).
Category: Number Theory
[1] viXra:2201.0002 [pdf] replaced on 2022-05-31 11:27:09
Authors: Federico Romagnoli
Comments: 35 Pages. English+Italian version
The aim of this paper is to show, through the regularities that emerge on composite numbers, some formal representations of primality, set of prime numbers and sequence of prime numbers. These regularities will also be seen in the context of the Riemann hypothesis. This work has been divided into three parts (paragraphs).
In the first part two formulas will be identified, defined in N_(>0)^2→N_(>8), that describe the infinite sequences of infinite composite odd numbers. On the basis of these formulas, two definitions will follow, both of primality and of sets of prime numbers. In addition, graphs will be used to better represent the results and the regularities that have emerged, as well as some examples on the efficiency of the formulas found for the purposes of primality.
In the second part, through an indicator function (or characteristic) and a generating function, we will try to represent a sequence of prime numbers starting both from the two primality definitions identified above, and from the simple definition of prime number.
In the third part we will try to generalize the two formulas found in the first part to domains other than N_(>0). The definitions given above will be adapted to the new formulas and, lastly, the results obtained will be analysed in the context of the Riemann hypothesis, an unprovable hypothesis. These are the conclusions.
Category: Number Theory
| Third-Party Links: |
|