相关论文: On the Landau-Siegel Zeros Conjecture

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

We offer a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on $\mathbb{R}^n$. We use this idea to extend the result to real hyperbolic spaces $\mathbb{H}^n$.

This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…

We derive the Euler-Lagrange equation corresponding to a variant of non-Euclidean constrained von Karman theories.

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We study a variant of algebraic K-theory and prove that it is stable and preserves module structures.

This is a survey on Kawaguchi-Silverman conjecture.

In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.

We propose a projective version of the celebrated Brauer's Height Zero Conjecture on characters of finite groups and prove it, among other cases, for $p$-solvable groups as well as for (some) quasi-simple groups.

Let $k\geq 2$ be an integer and let $\lambda$ be the Liouville function. Given $k$ non-negative distinct integers $h_1,\ldots,h_k$, the Chowla conjecture claims that $\sum_{n\leq x}\lambda(n+h_1)\cdots \lambda(n+h_k)=o(x)$ as $x\to\infty$.…

Under a weakened version of Hardy-Littlewood Conjecture on the number of representations in Goldbach problem, J. H. Fei proved bounds for the Siegel zeros. Recently G. Bhowmik and K. Halupczok generalized Fei's result under a weaker…

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.

We describe Greenberg's pseudo-null conjecture, and prove a result describing conditions under which the pseudo-null conjecture for a number field $K$ implies the conjecture for finite extensions of $K$. We then apply the result to the…

A new simple way to prove the Frobenius conjecture on the dimensions of real algebras without zero divisors is given.

In this paper the circulant Hadamard conjecture is proved.

In this paper, we give a simple counter example to the famous Hodge conjecture.