Related papers: On Bohr's equivalence theorem

In this note we prove a weighted version of the Khintchine inequalities.

In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel 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 prove the Aharoni Berger Conjecture

Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and…

We prove a result related to Dirichlet spectrum for simultaneous approximation to two real numbers in Euclidean norm and badly or very well approximability.

In this paper we show an index theorem for gerbes

We prove a new converse theorem for Borcherds' multiplicative theta lift which improves the previously known results. To this end we develop a newform theory for vector valued modular forms for the Weil representation, which might be of…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

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

We show that every set $A$ of natural numbers with positive upper density can be shifted to contain the restricted sumset $\{b_1 + b_2 : b_1, b_2\in B \text{ and } b_1 \neq b_2 \}$ for some infinite set $B \subset A$.

A simple necessary and sufficient condition is given for an absolutely convergent Dirichlet series with imaginary exponents and only real zeros to be a finite product of sines. The proof is based on Meyer's theorem on quasicrystals.

It is shown that the isomorphism relation between continuous t-norms is Borel bireducible with the relation of order isomorphism between linear orders on the set of natural numbers, and therefore, it is a Borel complete equivalence…

We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.

We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.

We prove a version of Dedekind's Transposition Principle that holds in lattices of equivalence relations.

We establish a q-analogue of Wolstenholme's harmonic series congruence.

A very simple but useful almost sure convergence theorem of probability is given.

We prove equivalences of derived categories for the various mirrors in the Batyrev-Borisov construction. In particular, we obtain a positive answer to a conjecture of Batyrev and Nill. The proof involves passing to an associated category of…

In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type [8]. We reported conditions which guarantee convergence…