Related papers: A generalization of Tur\'{a}n's theorem

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.

In this short expository article, we describe a mathematical tool called the probabilistic method, and illustrate its elegance and beauty through proving a few well-known results. Particularly, we give an unconventional probabilistic proof…

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

A generalization of the law of total covariance is presented and proved.

By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P. Sz\"usz we obtain a gap theorem which is more general then both these theorems.

In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].

We give a new proof of a theorem of B.M. Bredihin which was originally proved by extending Linnik's solution, via his dispersion method, of a problem of Hardy and Littlewood.

We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.

We prove an infinitary version of the Brauer-Schur theorem.

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.

We prove some new results related to Tanaka's formula.

I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.

A new generalization of the classical separate algebraicity theorem is suggested and proved.

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.