Related papers: On two Kuznetsov's conjectures
In this paper, we proved a special case of the DDVV Conjecture.
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
An technically interesting proof of a known theorem.
We provide a proof of the Borwein Conjecture using analytic methods.
In [2] the author claims to provide a counterexample to a result in a recent paper [1]. In this note, we prove that the details of his example is false and this example is compatible with our result in [1] and so is not a countreexample.
We settle in the affirmative the Graham-Sloane conjecture.
We obtain some new inequalities of Chebyshev Type.
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
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.
An integral transformation relating two inequalities in Khabibullin's conjecture is found. Another proof of this conjecture for some special values of its numeric parameters is suggested.
We illustrate the concept of mathematical proof.
We prove two polynomial identities which are particular cases of a conjecture arising in the theory of L-functions of twisted Carlitz modules. This conjecture is stated in earlier papers of the second author.
We prove a conjecture on Rubin-Stark elements, which was recently proposed by the author, and also by Mazur and Rubin, in a special case.
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
We establish an expansion theory for $\text{SL}_2(\mathbb Z/q\mathbb Z)$. Incorporating this into a framework recently developed by Shkredov, we confirm Zaremba's conjecture.
By creating a new method, the author proved the well-known world's baffling problems Goldbach conjecture, twin primes conjecture, the Proposition (C) and the Proposition $n^2+1$.
A proposed solution to the Riemann Hypothesis
We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne) for the relation between the two natural products on the space of Chinese characters. The…
A counter example to the main result has been communicated to the author by Matei Toma.