Related papers: The Hasse norm principle for abelian extensions --…
A finite extension of global fields $L/K$ satisfies the Hasse norm principle if any nonzero element of $K$ has the property that it is a norm locally if and only if it is a norm globally. In 1931, Hasse proved that any cyclic extension…
This note corrects a minor misstatement in section 2 of the paper in the title (arXiv:0808.3426). It also addresses some related issues. The error does not affect the main results of that paper, but nevertheless this corrigendum seems…
In this paper we establish a Hasse principle concerning the linear dependence over $\Z$ of nontorsion points in the Mordell-Weil group of an abelian variety over a number field.
In this paper we show the Hasse principle for the Brauer group of a purely transcendental extension field in one variable over an arbitrary field.
This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].
In our paper "Essential normality, essential norms and hyperrigidity" we claimed that the restriction of the identity representation of a certain operator system (constructed from a polynomial ideal) has the unique extension property,…
In this paper has been withrawn by the author due the error in the proof of theoem 1.
By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables.
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
The proofs of Theorem 3.1 and Corollary 4.1 in Le\~ao and Ohashi (2013) are incomplete. The reason is a wrong statement in Remark 2.2. The hypotheses and statements of Theorem 3.1 and Corollary 4.1 in Le\~ao and Ohashi (2013) remain…
Let L_1 and L_2 be finite abelian extensions of a global field K. We compute the obstruction to the multinorm principle for the pair L_1, L_2.
In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted…
With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree d polynomials f that are ordered by height. This allows us to establish averaged versions of the Bateman-Horn conjecture, the…
The arguments of the above article [arXiv:0910.3934] do not apply to the papers which it criticizes, and contain several key errors, including a fundamental misunderstanding about the equivalence principle.
We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…
We unite two themes in dyadic analysis and number theory by studying an analogue of the failure of the Hasse principle in harmonic analysis. Explicitly, we construct an explicit family of measures on the real line that are $p$-adic and…
In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel functions of the first kinds are established
For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field.
There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.
Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…