论文标题
关于用公共分子的圆形移动分数的残留物
On residues of rounded shifted fractions with a common numerator
论文作者
论文摘要
对于任何正整数$ n $以及参数$α$和$ν$的参数，我们定义和调查$α$缩短，$ν$ -offset，长度$ n $的地板序列。我们发现在特定一致性类别中的序列中，整数数量的精确和渐近公式。正如我们将看到的那样，这些数量与计算圆锥截面界面区域中包含的晶格点的某些问题有关。我们为椭圆形区域中包含的晶格点的数量提供了具体示例，并与几个知名的整数环（包括高斯整数和艾森斯坦整数）建立了连接。
For any positive integer $n$ along with parameters $α$ and $ν$, we define and investigate $α$-shifted, $ν$-offset, floor sequences of length $n$. We find exact and asymptotic formulas for the number of integers in such a sequence that are in a particular congruence class. As we will see, these quantities are related to certain problems of counting lattice points contained in regions of the plane bounded by conic sections. We give specific examples for the number of lattice points contained in elliptical regions and make connections to a few well-known rings of integers, including the Gaussian integers and Eisenstein integers.
