Related papers: A note on the quantum Wielandt inequality

We show that the Schur polynomials in all primitive $n$th roots of unity are $1$, $0$, or $-1$, if $n$ has at most two distinct odd prime factors. This result can be regarded as a generalization of properties of the coefficients of the…

In 1927, E. Artin conjectured that all non-square integers $a\neq -1$ are a primitive root of $\mathbb{F}_p$ for infinitely many primes $p$. In 1967, Hooley showed that this conjecture follows from the Generalized Riemann Hypothesis (GRH).…

The celebrated Artin conjecture on primitive roots asserts that given any integer $g$ which is neither $-1$ nor a perfect square, there is an explicit constant $A(g)>0$ such that the number $\Pi(x;g)$ of primes $p\le x$ for which $g$ is a…

Let $F$ be a local field and let $R$ be its ring of integers. For a positive integer $n$, an integral quadratic form defined over $R$ is called primitively $n$-universal if it primitively represents all quadratic forms of rank $n$. It was…

In 1981, Sacks and Uhlenbeck introduced their famous $\alpha$-energy as a way to approximate the Dirichlet energy and produce harmonic maps from surfaces into Riemannian manifolds. However, the second and third authors together with…

A nonnegative matrix A is said to be primitive if there exists a positive integer m such that entries in A^m are positive and smallest such m is called the exponent of A: Primitive matrices are useful in the study of finite Markov chains…

Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…

A C*-algebra is called primitive if it admits a faithful and irreducible *-representation. We show that if A_1 and A_2 are separable, unital, residually finite dimensional C*-algebras that are not both two dimensional, then their unital…

In this note we study common preperiodic points of rational maps of the Riemann Sphere. We show that given any degrees $d_1,d_2\geq2$, outside a Zariski closed subset of the space of pairs of rational maps $(f,g)$ of degree $d_1$ and $d_2$…

In this paper we prove two results. The first shows that the Dirichlet-Neumann map of the operator $\Delta_g+q$ on a Riemannian surface can determine its topological, differential, and metric structure. Earlier work of this type assumes a…

Primitive equivalence of graphs and matrices was used by Enomoto, Fujii and Watatani to classify Cuntz-Krieger algebras of 3x3 irreducible matrices. In this paper it is shown that the definition of primitive equivalence can be simplified…

In Baraka's paper [2], he obtained the Littlewood-Paley characterization of Campanato spaces $L^{2,\lambda}$ and introduced $\mathcal {L}^{p,\lambda,s}$ spaces. He showed that $\mathcal…

A set of positive integers is primitive (or 1-primitive) if no member divides another. Erd\H{o}s proved in 1935 that the weighted sum $\sum1/(n \log n)$ for $n$ ranging over a primitive set $A$ is universally bounded over all choices for…

Refining some results of S. S. Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is…

For a bounded Lipschitz domain $\Sigma$ in a Riemannian surface $M$ satisfying certain curvature condition, we prove that $$\mu_{3-\beta_1} \leq \lambda_{1},$$ where $\mu_k$ ($\lambda_k$ resp.) is the $k$-th Neumann (Dirichlet resp.)…

The aim of this paper is to establish some properties of solutions to the Dirichlet-Neumann problem: $(\partial_z\partial_{\overline{z}})^2 w=g$ in the unit disc $\ID$, $w=\gamma_0$ and…

We prove a weak-type (1,1) inequality for square functions of non-commutative martingales that are simultaneously bounded in $L^2$ and $L^1$. More precisely, the following non-commutative analogue of a classical result of Burkholder holds:…

We investigate certain immersions of constant curvature from Riemann surfaces into flag manifolds equipped with invariant metrics, namely primitive lifts associated to pseudoholomorphic maps of surfaces into complex Grassmannians. We prove…

This work is a contribution to the classification of Teichm\"uller curves in the moduli space $\M_2$ of Riemann surfaces of genus 2. While the classification of primitive Teichm\"uller curves in $\M_2$ is complete, the classification of the…

Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for…