Related papers: An Arithmetic Metric
What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture that every distribution with a density function whose…
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
We begin with an interpretation of the L1-distance between two power spectral densities and then, following an analogous rationale, we develop a natural metric for quantifying distance between respective covariance matrices.
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
A new definition of a real number is that it is a rule which says Yes or No based on whether the real number ought to be in a given rational interval. This is a teaser paper for formalizing, exploring, and generalizing this definition. The…
We give a simple naming argument for establishing lower bounds on the combinatorial distance between (positive) braid words.
Statistical distribution of the primes in an arithmetic progression is considered. The estimation of prime numbers is given and combinatorial methods are used to calculate the twin primes on the available interval. The distribution and…
In this work I look at the distribution of primes by calculation of an infinite number of intersections. For this I use the set of all numbers which are not elements of a certain times table in each case. I am able to show that it exists a…
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense…
An alternating distance is a link invariant that measures how far away a link is from alternating. We study several alternating distances and demonstrate that there exist families of links for which the difference between certain…
Prime numbers have attracted the attention of mathematiciansand enthusiasts for millenniums due to their simple definition and remarkable properties. In this paper, we study primorial numbers (the product of the first prime numbers) to…
Here is a square problem: in a unit square, is there a point with four rational distances to the vertices? A probability argument suggests a negative answer. This paper proves several special cases of the square problem: if the point sits…
In this paper the characterization as convolution operators of filters sending finite energy signals to bounded signals is used to prove several theoretical results concerning the distance between the ideal filter and the spaces of…
In this article some difficulties are deduced from the set of natural numbers. By using the method of transfinite recursion we define an iterative process which is designed to deduct all the non-greatest elements of the set of natural…
In this paper, we will show that the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers is unusually large. This generalizes the very recent results by the author and by A. Dubickas, which are both…
In this paper, we derive formulas for the analytical calculation of the moments of the distance between two uniformly and independently distributed random points in an $n$-sided regular polygon. A number of closed form expressions is…
Given two binary trees on $N$ labeled leaves, the quartet distance between the trees is the number of disagreeing quartets. By permuting the leaves at random, the expected quartets distance between the two trees is…
We introduce the notion of the cosmic numbers of a cosmological model, and discuss how they can be used to naturally classify models according to their ability to solve some of the problems of the standard cosmological model.
We present some new ideas on important problems related to primes. The topics of our discussion are: simple formulae for primes, twin primes, Sophie Germain primes, prime tuples less than or equal to a predefined number, and their…
In this paper, we show a new upper bound of prime gaps, that is the gap between a prime number and its consecutive prime number. We show that the gap between a prime number $p_n$ and its consecutive prime number is not larger than…