相关论文: Generalizations of an Ancient Greek Inequality abo…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
The Schinzel Hypothesis is a celebrated conjecture in number theory linking polynomial values and prime numbers. In the same vein we investigate the common divisors of values $P_1(n),\ldots, P_s(n)$ of several polynomials. We deduce this…
Arthur Cohn's irreducibility criterion for polynomials with integer coefficients and its generalization connect primes to irreducibles, and integral bases to the variable $x$. As we follow this link, we find that these polynomials are ready…
In the present paper, we have developed a method for solving \textit{diophantine inequalities} using their relationship with the \textit{difference between consecutive primes}. Using this approach we have been able to prove some theorems,…
Majorization inequalities for symmetric polynomials have interested mathematicians for centuries, from the AM-GM inequality for two variables going back at least to Euclid, through classical results of Newton, Muirhead and Gantmacher, to…
We speculate on the distribution of primes in exponentially growing, linear recurrence sequences $(u_n)_{n\geq 0}$ in the integers. By tweaking a heuristic which is successfully used to predict the number of prime values of polynomials, we…
We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titchmarsh inequality.
We resolve the function field analogue of the conjecture concerning distribution of twin primes in arithmetic progression.
We extend the inequality of Audenaert et al to general von Neumann algebras.
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.
Polignac [1] conjectured that for every even natural number $2k (k\geq1)$, there exist infinitely many consecutive primes $p_n$ and $p_{n+1}$ such that $p_{n+1}-p_n=2k$. A weakened form of this conjecture states that for every $k\geq1$,…
Positive polynomials arising from Muirhead's inequality, from classical power mean and elementary symmetric mean inequalities and from Minkowski's inequality can be rewritten as sums of squares.
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…
We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors(arXiv:math.NT/0605563).
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward…
In this paper we collect some results about arithmetic progressions of higher order, also called polynomial sequences. Those results are applied to $(m,q)$-isometric maps.
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…