Related papers: One-dimensional quasi-uniform Kronecker sequences

We study the asymptotic consistency properties of $\alpha$-R\'enyi approximate posteriors, a class of variational Bayesian methods that approximate an intractable Bayesian posterior with a member of a tractable family of distributions, the…

We develop the inhomogeneous counterpart to some key aspects of the story of the Duffin--Schaeffer Conjecture (1941). Specifically, we construct counterexamples to a number of candidates for a sans-monotonicity version of Szusz's…

We prove that every compact K\"ahler threefold $X$ of Kodaira dimension $\kappa = 0$ or $1$ has a $\mathbf{Q}$-factorial bimeromorphic model $X'$ with at worst terminal singularities such that for each curve $C \subset X'$, the pair…

Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663--688, 2005.]. This article considers the basic properties that a…

We study what Jordan-Kronecker invariants of Lie algebras, introduced by A. V. Bolsinov and P. Zhang, are possible. We completely solve this problem in the Jordan and the Kronecker cases. We prove that any JK invariants that contain the…

Let $K_{q^n}(a)$ be a Kloosterman sum over the finite field $\F_{q^n}$ of characteristic $p$. In this note so called subfield conjecture is proved in case $p>3$: if $a\ne0$ belongs to the proper subfield $\F_q$ of $\F_{q^n}$, then…

The Euler-Mascheroni constant $\gamma=0.5772\dots\!$ is the $K=\mathbb{Q}$ example of an Euler-Kronecker constant $\gamma_K$ of a number field $K.$ In this note we consider the size of the $\gamma_q=\gamma_{K_q}$ for cyclotomic fields…

Let $G$ be a connected unimodular group equipped with a (left and hence right) Haar measure $\mu_G$, and suppose $A, B \subseteq G$ are nonempty and compact. An inequality by Kemperman gives us…

We prove asymptotic 0-1 Laws satisfied by diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane, and the upper boundary is called the shape. For various types, we show that, as the…

We introduce an expansion formula for elements in quantum cluster algebras associated to type A and Kronecker quivers with principal quantization. Our formula is parametrized by perfect matchings of snake graphs as in the classical case. In…

Let $X$ be a finite CW complex and let $h_1, h_2: C(X)\to A$ be two unital \hm s, where $A$ is a unital C*-algebra. We study the problem when $h_1$ and $h_2$ are approximately homotopic. We present a $K$-theoretical necessary and sufficient…

We prove that N\'eron models of jacobians of generically-smooth nodal curves over bases of arbitrary dimension are quasi-compact (hence of finite type) whenever they exist. We give a simple application to the orders of torsion subgroups of…

In this paper, we show that a locally constant cocycle $\mathcal{A}$ is $k$-quasi multiplicative under the irreducibility assumption. More precisely, we show that if $\mathcal{A}^t$ and $\mathcal{A}^{\wedge m}$ are irreducible for every $t…

It is known that for every $\alpha \geq 1$ there is a planar triangulation in which every ball of radius $r$ has size $\Theta(r^\alpha)$. We prove that for $\alpha <2$ every such triangulation is quasi-isometric to a tree. The result…

While Kronecker coefficients $g(\lambda,\mu,\nu)$ with bounded rows are polynomial-time computable via lattice-point methods, no explicit closed-form formulas have been obtained for genuinely three-row cases in the 87 years since…

Digital Kronecker-sequences are a non-archimedean analog of classical Kronecker-sequences whose construction is based on Laurent series over a finite field. In this paper it is shown that for almost all digital Kronecker-sequences the star…

A sequence of rational functions in a variable $q$ is $q$-holonomic if it satisfies a linear recursion with coefficients polynomials in $q$ and $q^n$. We prove that the degree of a $q$-holonomic sequence is eventually a quadratic…

In this paper we prove that if (u, K) is an almost-minimizer of the Griffith functional and K is $\epsilon$-close to a plane in some ball B $\subset$ R N while separating the ball B in two big parts, then K is C 1,$\alpha$ in a slightly…

A $k$-uniform hypergraph is $s$-almost intersecting if every edge is disjoint from exactly $s$ other edges. Gerbner, Lemons, Palmer, Patk\'os and Sz\'ecsi conjectured that for every $k$, and $s>s_0(k)$, every $k$-uniform $s$-almost…

Kurzweil's theorem ('55) is concerned with zero-one laws for well approximable targets in inhomogeneous Diophantine approximation under the badly approximable assumption. In this article, we prove the divergent part of a Kurzweil type…