论文标题
使用广义类密度函数生成圆的亚组
Generating Subgroups of the Circle using a Generalized class of Density Functions
论文作者
论文摘要
在本文中，我们考虑\ cite {bdk}中引入的自然密度函数的广义版本$ d^f_g $其中$ g：\ n \ rightarrow [0，\ infty）$满足$ g（n）\ rightarrow \ rightarrow \ rightarrow \ rightarrow \ infty \ infty $ and $ \ frac {n} n} n} g（n）使用这些密度函数生成圆组$ \ t $的特征子组的版本。我们表明，这些子组具有与$ s $特征的子组\ cite {ddb}或$α$ characteratized子群体\ cite {bdh}相同的功能，我们的结果为两篇文章的主要结果提供了更一般的版本。但是，与此同时，这种更通用的方法的实用性是通过构建新的和非平凡的亚组的合适选择来选择$ f $和$ g $的。在我们的几个结果中，我们使用了理想$ \ iz_g（f）$的属性，这些属性首先呈现，以及对这些理想的某些新观察结果，这些观察是\ cite {bdk}中不存在的。
In this article, we consider the generalized version $d^f_g$ of the natural density function introduced in \cite{BDK} where $g : \N \rightarrow [0,\infty)$ satisfies $g(n) \rightarrow \infty$ and $\frac{n}{g(n)} \nrightarrow 0$ whereas $f$ is an unbounded modulus function and generate versions of characterized subgroups of the circle group $\T$ using these density functions. We show that these subgroups have the same feature as the $s$-characterized subgroups \cite{DDB} or $α$-characterized subgroups \cite{BDH} and our results provide more general versions of the main results of both the articles. But at the same time the utility of this more general approach is justified by constructing new and nontrivial subgroups for suitable choice of $f$ and $g$. In several of our results we use properties of the ideal $\iZ_g(f)$ which are first presented along with certain new observations about these ideals which were not there in \cite{BDK}.
