Related papers: A new proof of Vantieghem's theorem

We present a new, elementary, dynamical proof of the prime number theorem.

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.

We give a new elementary proof of Landau's Prime Ideal Theorem. The proof is an extension of Richter's proof of the Prime Number Theorem. The main result contains other results related to the equidistribution of the prime ideal counting…

In this note we shall give a new proof to a quadrature formulae due to Newton.

In this paper, we introduce two primality tests based on new divisibility properties of binomial coefficients. These new properties were enunciated and proved in previous work. We also study two similar tests that can be obtained from…

We give a new proof of Fitzgerald's criterion for primitive polynomials over a finite field. Existing proofs essentially use the theory of linear recurrences over finite fields. Here, we give a much shorter and self-contained proof which…

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

This is an exposition, in 12 pages including all prerequisites and a generalization, of Karamata's little known elementary proof of the Landau-Ingham Tauberian theorem, a result in real analysis from which the Prime Number Theorem follows…

We present a proof given by Euler in his paper {\it ``De serierum determinatione seu nova methodus inveniendi terminos generales serierum"} \cite{E189} (E189:``On the determination of series or a new method of finding the general terms of…

We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

A vector variational principle is proved.

We give a new sufficient condition which allows to test primality of Fermat's numbers. This characterization uses uniquely values at most equal to tested Fermat number. The robustness of this result is due to a strict use of elementary…

A new elementary proof of the prime number theorem presented recently in the framework of a scale invariant extension of the ordinary analysis is re-examined and clarified further. Both the formalism and proof are presented in a much more…

An technically interesting proof of a known theorem.

Let $\Omega(n)$ denote the number of prime factors of $n$. We show that for any bounded $f\colon\mathbb{N}\to\mathbb{C}$ one has \[ \frac{1}{N}\sum_{n=1}^N\, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N\, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1).…

We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].

Dirichlet's theorem on arithmetic progressions called as Dirichlet prime number theorem is a classical result in number theory. Atle Selberg\cite{Selberg} gave an elementary proof of this theorem. In this article we give an alternative…

Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin's classical proof of Euler's pentagonal number theorem.