A simple polynomial for a simple transposition

中心单代数中具有给定特征多项式的格点计数

Counting lattice points in central simple algebras with a given characteristic polynomial

本文将Eskin, Mozes和Shah于1996年提出的计数具有给定不可约特征多项式整数矩阵的渐近公式，推广至特定中心单代数极大序中的元素计数情形。

Characteristic polynomials of central simple algebras

We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description of separable conjugacy classes of the multiplicative group.

A simple proof of a congruence for a series involving the little $q$-Jacobi polynomials

We give a simple and a more explicit proof of a mod $4$ congruence for a series involving the little $q$-Jacobi polynomials which arose in a recent study of a certain restricted overpartition function.

Characteristic Polynomials of Simple Ordinary Abelian Varieties over Finite Fields

We provide an easy method for the construction of characteristic polynomials of simple ordinary abelian varieties ${\mathcal A}$ of dimension $g$ over a finite field ${\mathbb F}_q$, when $q\ge 4$ and $2g=ρ^{b-1}(ρ-1)$ for some prime $ρ\ge 5$, with $b\ge 1$. Moreover, we show that ${\mathcal A}$ is absolutely simple if $b=1$ and $ρ=5$, but ${\mathcal A}$ is not absolutely simple for arbitrary $ρ$ with $b>1$.