arXiv subjects

Lubomir Alexandrov

Publications and source records attributed to Lubomir Alexandrov.

4 recordsLinked to original sources

arXiv2004

Prime Number Diffeomorphisms, Diophantine Equations and the Riemann Hypothesis

We explicitly construct a diffeomorphic pair (p(x),p^{-1}(x)) in terms of an appropriate quadric spline interpolating the prime series. These continuously differentiable functions are the smooth analogs of the prime series and the prime counting function, respectively, and contain the basic information about the specific behavior of the primes. We employ p^{-1}(x) to find approximate solutions of Diophantine equations over the primes and discuss how this function could eventually be used to analyze the von Koch estimate for the error in the prime number theorem which is known to be equivalent to the Riemann hypothesis.

math-ph↗

arXiv2003

Prime number logarithmic geometry on the plane

We found a regularity of the behavior of primes that allows to represent both prime and natural numbers as infinite matrices with a common formation rule of their rows. This regularity determines a new class of infinite cyclic groups that permit the proposition a plane--spiral geometric concept of the arithmetic.

math.GM↗

arXiv2001

The Eratosthenes Progression p_{k+1} = π^{-1}(p_k), k=0,1,2,..., p_0 \in N \setminus P Determines An Inner Prime Number Distribution Law

Formulas of $π(x)$-fine structure are presented.

math.NT↗

arXiv1998

On the nonasymptotic prime number distribution

The objective of this paper is to introduce an approach to the study of the nonasymptotic distribution of prime numbers. The natural numbers are represented by theorem 1 in the matrix form ^2N. The first column of the infinite matrix ^2N starts with the unit and contains all composite numbers in ascending order.The infinite rows of this matrix except for the first elements contain prime numbers only, which are determined by an uniform recurrence law. At least one of the elements of the twin pairs of prime numbers is an element of the second column of the matrix ^2N (theorem 3). The basic information on the nonasymptotic prime number distribution is contained in the distribution of the elements of the second column of the matrix ^2N.

math.NT↗