Related papers: A Dynamical Proof of the Prime Number Theorem

We will present a new proof of the Gromoll-Grove diameter rigidity theorem.

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

We give an elementary proof to Hasse theorem.

We give a counting based proof of the Graham Pollak Theorem

We prove that there are infinitely many integers $n$ such that $n$ and $n+1$ have the same number of distinct prime divisors.

We prove the analog of Cram\'er's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based…

We continue our recent work on averages for ternary additive problems with powers of prime numbers.

We give a new, elementary proof of the celebrated Herzog-Hibi-Zheng theorem on powers of quadratic monomial ideals.

In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in…

This is a new proof of the tauberian theorem of complex Laplace transformation for getting a simple proof of the prime numbers theorem $\pi(x) \sim \frac{x}{\log(x)}$ for a largest real $x$.

Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

A vector variational principle is proved.

Let $f(x)\in \mathbb{Z}[x]$ be an irreducible polynomial of degree $d\ge 1$. Let $k\ge2$ be an integer. The number of integers $n$ such that $f(n)$ is $k$-free is widely studied in the literature. In principle, one expects that $f(n)$ is…

{\bf In the fourth extended version of this article, we provide a comprehensive historical survey of 200 different proofs of famous Euclid's theorem on the infinitude of prime numbers (300 {\small B.C.}--2022)}. The author is trying to…

We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation

Euclid's proof can be reworked to construct infinitely many primes, in many different ways, using ideas from arithmetic dynamics. After acceptance Soundararajan noted the beautiful and fast converging formula: $$ \tau = a^{1/(d-1)} x_0…

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…