相关论文: On Hadamard Conjecture

This paper has been withdrawn by the authors, the main result being known since Lam and Leung, J. Algebra 2000.

We discuss an extension of the almost Hadamard matrix formalism, to the case of complex matrices. Quite surprisingly, the situation here is very different from the one in the real case, and our conjectural conclusion is that there should be…

We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.

In this paper, we proved a special case of the DDVV Conjecture.

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

This note provides a self-contained exposition of the proof of the artinian conjecture, following closely Djament's Bourbaki lecture. The original proof is due to Putman, Sam, and Snowden.

This note is a somewhat-lighthearted comment on a recent paper by David Wallace, arXiv:0906.2718[quant-ph] entitled "A formal proof of the Born rule from decision-theoretic assumptions".

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

We present a proof of Hadamard Inverse Function Theorem by the methods of Variational Analysis, adapting an idea of I. Ekeland and E. Sere.

We analyze the physical aspects and origins of currently proposed oracles for (absolute) randomness.

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…

The paper presents a counterexample to the Hodge conjecture.

This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…

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

This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576

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

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…

This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…

We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005].