Related papers: On Hadamard Conjecture
In this paper the circulant Hadamard conjecture is proved.
Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…
It is shown that if $H$ is a circulant Hadamard $4n\ti 4n $ then $n=1$. This proves the Hadamard circulant conjecture.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We give a new proof of Theorem 6 in [L. Qiu and X. Zhan, On the span of Hadamard products of vectors, Linear Algebra Appl. 422 (2007) 304--307].
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…
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
The Ramanujan conjecture for modular forms of holomorphic type was proved by Deligne almost half a century ago: the proof, based on his earlier proof of Weil's conjectures, was an achievement of algebraic geometry. We give here a short…
We describe an approach to the circulant Hadamard conjecture based on Walsh-Fourier analysis. We show that the existence of a circulant Hadamard matrix of order $n$ is equivalent to the existence of a non-trivial solution of a certain…
This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.
First examples of symmetric Hadamard matrices of orders 508 and 764 are constructed. The method used is known as the propus construction. A conjecture regarding this method is formally proposed but it appears implicitly in three previous…
In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
This is a survey on Sarnak's Conjecture
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
In this paper, a conjecture of Mazur, Rubin and Stein concerning certain averages of modular symbols is proved.