相关论文: The reciprocal algebraic integers having small hou…

The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geometric information about the length of reciprocal geodesics, as…

We study the category of graded representations with finite--dimensional graded pieces for the current algebra associated to a simple Lie algebra. This category has many similarities with the category $\cal O$ of modules for $\lie g$ and in…

Let $\chi$ be an order $c$ multiplicative character of a finite field and $f(x)=x^d+\lambda x^e$ a binomial with $(d,e)=1$. We study the twisted classical and $T$-adic Newton polygons of $f$. When $p>(d-e)(2d-1)$, we give a lower bound of…

We explain how a slight variant in the use of our recursive algorithm leads to improve the known lower bounds for the absolute trace of a totally positive algebraic integer. We also link the absolute trace of a totally positive algebraic…

Let $P$ be a commutative Noetherian ring and $F$ be a self-dual acyclic complex of finitely generated free $P$-modules. Assume that $F$ has length four and $F_0$ has rank one. We prove that $F$ can be given the structure of a Differential…

Let ${\cal P}_n^c$ denote the set of all algebraic polynomials of degree at most $n$ with complex coefficients. Let $$D^+ := \{z \in \mathbb{C}: |z| \leq 1, \, \, \Im(z) \geq 0\}$$ be the closed upper half-disk of the complex plane. For…

In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. For idempotent algebras we give a simple criteria for the…

The problem of finding provably maximal sets of mutually unbiased bases in $\mathbb{C}^d$, for composite dimensions $d$ which are not prime powers, remains completely open. In the first interesting case, $d=6$, Zauner predicted that there…

Let $D>1$ be an integer, and let $b=b(D)>1$ be its smallest divisor. We show that there are infinitely many number fields of degree $D$ whose primitive elements all have relatively large height in terms of $b$, $D$ and the discriminant of…

Let $K$ be an algebraically closed field that is complete with respect to a non-Archimedean absolute value, and let $\varphi\in K(z)$ have degree $d\geq 2$. We characterize maps for which the minimal resultant of an iterate $\varphi^n$ is…

We prove that over an algebraically closed field $\mathbb{K}$ of characteristic different from $2$, the group algebra $R=\mathbb{K} D_\infty$ of the infinite dihedral group $D_\infty$ has exactly six conjugacy classes of involutions…

The repetition threshold is the smallest real number $\alpha$ such that there exists an infinite word over a $k$-letter alphabet that avoids repetition of exponent strictly greater than $\alpha$. This notion can be generalized to graph…

If $a$ and $d$ are relatively prime, we refer to the set of integers congruent to $a$ mod $d$ as an `eligible' arithmetic progression. A theorem of Dirichlet says that every eligible arithmetic progression contains infinitely many primes;…

We determine the decomposition numbers of the partition algebra when the characteristic of the ground field is zero or larger than the degree of the partition algebra. This will allow us to determine for which exact values of the parameter…

Recently there has been quite a bit of study carried out related to arithmetic properties of overpartitions into non-multiples of two co-prime integers. The paper [19] by Nadji et al. looked into congruences modulo $3$ and powers of $2$ for…

Let $\alpha$ be a complex number. We show that there is a finite subset $F$ of the ring of the rational integers $\mathbb{Z}$, such that $F\left[ \alpha\right] =\mathbb{Z}\left[ \alpha\right]$, if and only if $\alpha$ is an algebraic number…

We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal field theories, affine Kac-Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix $S$, we find…

Let $A$ be a Poisson Hopf algebra over an algebraically closed field of characteristic zero. If $A$ is finitely generated and connected graded as an algebra and its Poisson bracket is homogeneous of degree $d \geq 0$, then $A$ is…

Let ${\mathcal D}(n)$ be the maximal determinant for $n \times n$ $\{\pm 1\}$-matrices, and $\mathcal R(n) = {\mathcal D}(n)/n^{n/2}$ be the ratio of ${\mathcal D}(n)$ to the Hadamard upper bound. Using the probabilistic method, we prove…

This work shows that the smallest natural number $d_n$ that is not the determinant of some $n\times n$ binary matrix is at least $c\,2^n/n$ for $c=1/201$. That same quantity naturally lower bounds the number of distinct integers $D_n$ which…