Related papers: On Ryser's Conjecture

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

We survey recent developments on the Restriction conjecture.

New cases of the multiplicity conjecture are considered.

The paper presents several new sufficient conditions, as well as new equivalent criteria for the classical Riemann Hypothesis. Noteworthy are also other statements and remarks about $\zeta$ to be found throughout the paper.

The Riemann hypothesis (RH) is well known. In this paper we would show some sufficient conditions for the RH. The first condition is related with the sum of divisors function and another one is related with the Chebyshev's function.

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.

We prove the Aharoni Berger Conjecture

We give a new equivalent condition for the Riemann hypothesis consisting in an order condition for certain finite rational combinations of the values of the Riemann zeta-function at even positive integers.

We give a proof of some small weight and level cases of Serre's conjecture.

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

The article presents the proof of Casas-Alvero conjecture.

We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We prove several extensions of the Erdos-Fuchs theorem.

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