相关论文: On Vojta's $1+\epsilon$ Conjecture

In their recent article, Min Ru and Paul Vojta, among other things, proved the so-called general theorem (arithmetic part) which can be viewed as an extension of Schmidt's subspace theorem. In this note, we extend their result by replacing…

The connection between inequalities in additive combinatorics and analogous versions in terms of the entropy of random variables has been extensively explored over the past few years. This paper extends a device introduced by Ruzsa in his…

The purpose of this erratum is to correct a mistake in the proof of Theorem 4.1 of our paper \cite{CF}.

(a few typos and an error corrected)

I point out and diagnose an error in a figure in a textbook on classical physics. The error helps to illustrate a pitfall encountered when dealing with the shapes of objects, and perhaps also reflects general cultural attitudes in physics.…

The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…

We formulate Vojta's conjecture for smooth weighted projective varieties, weighted multiplier ideal sheaves, and weighted log pairs and prove that all three versions of the conjecture are equivalent. In the process, we introduce generalized…

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

A Comment on the letter by V. Koptev, et al. - Phys. Rev. Lett. 87 (2001) 022301.

Paul Erdos conjectured that for every n in N, n>1, there exist a, b, c natural numbers, not necessarily distinct, so that 4/n=1/a+1/b+1/c (see \cite{rg}). In this paper we prove an extension of Mordell's theorem and formulate a conjecture…

This note is an erratum to the paper "Tautological classes on moduli spaces of hyper-K\"ahler manifolds." Thorsten Beckman and Mirko Mauri have pointed to us a gap in the proof of \cite[Theorem 8.2.1]{Duke}. We do not know how to correct…

The purpose of [1] was as follows. ?We consider special sets of continuants which occur in applications. For these sets we solve the problem of finding maximal and minimal continuants. There are several methods for finding extremum such as…

This is an erratum to our paper in Physical Review D82:022004,2010, corresponding to preprint: arXiv:1003.2961 .

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…

In this article we define a minor relation, which is stronger than the classical one, but too strong to become a well-quasi-order on the class of finite graphs. Nevertheless, with this terminology we are able to introduce a conjecture,…

This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

The equations in cond-mat/0011020 and Phys. Rev, Lett. 86, 4652 (2001) are valid but a numerical estimate in the paper is incorrect.

I have noted a number of errors, most of them quite minor, in the {\em Encyclopedia of Cosmology} (New York and London: Garland), 1993, Norriss S. Hetherington, ed. The majority occur in my mathematically verbose article, ``Fundamental…

We prove a conjecture by Ruzsa from 2006 on a discrete version of the Brunn-Minkowski inequality, stating that for any $A,B\subset\mathbb{Z}^k$ and $\epsilon>0$ with $B$ not contained in $n_{k,\epsilon}$ parallel hyperplanes we have…