Related papers: Remarks on Robin's and Niocolas Inequalities
First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…
New cases of the multiplicity conjecture are considered.
We survey recent developments on the Restriction conjecture.
In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $\sigma(n)<e^\gamma n\log\log n$ holds for every integer $n>5040$, where $\sigma(n)$ is the sum of divisors function, and $\gamma$ is the…
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
The achievement of this paper is a confutation of the inequality addressed by the Nicolas criterion for the Riemann Hypothesis, carried out after establishing properties of two related sequences. One of them is the product…
We prove some extensions of Andrews inequality.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
We discuss various recent advances on weak forms of the Twin Prime Conjecture.
We discuss recent versions of the Brunn-Minkowski inequality in the complex setting, and use it to prove the openness conjecture of Demailly and Koll\'ar.
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
The paper presents a counterexample to the Hodge conjecture.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.