Related papers: Remarks on Robin's and Niocolas Inequalities

We address ZFC inequalities between some cardinal invariants of the continuum, which turned to be true in spite of strong expectations given by [RoSh:470].

The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove various cases of the Image Conjecture and show how it leads to…

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

Preliminary results from Nathanson [5] are used to prove the Muirhead and Rado inequalities.

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.

Nicolas' criterion for the Riemann Hypothesis (RH) is an inequality based on primorials and the Euler totient function. The aim of this paper is to reformulate Nicolas' criterion and prove the equivalent statement. I will show that the…

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

We prove the Aharoni Berger Conjecture

Six conjectures on pairs of consecutive primes are listed in this paper, together with examples for each case.

We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…

We upgrade Howard's divisibility toward Perrin-Riou's Heegner point Main Conjecture to an equality under some mild conditions. We do this by exploiting Wei Zhang's proof of the Kolyvagin conjecture. The main ingredient is an improvement of…

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

We extend Carpi's results by showing that Dejean's conjecture holds for n >= 30.

We prove an improved form of an expectation of Polya and discuss several related questions

In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture…

In this paper the circulant Hadamard conjecture is proved.

In this paper, we prove a conjecture of Schnell in the surface case.

In the paper we show the equality between the Lempert function and the Green function with two poles with equal weights in the bidisc thus giving the positive answer to a conjecture of Coman in the simplest unknown case. Actually, a…