论文标题
翻译沿模块表面膨胀的封闭震圈的理性点
Translates of rational points along expanding closed horocycles on the modular surface
论文作者
论文摘要
我们研究了在水平翻译下沿模块化表面上闭合的骨圈膨胀的序列的理性点的限制分布。使用光谱方法，我们确认当骨动感序列在一定的多项式范围内扩展时，确认这些样品点的等分分配。我们表明，等分分配失败的通用翻译失败，并且扩大速度略高。我们还通过获得明确的限制措施，同时允许肉眼伴侣的顺序快速扩展，我们还通过获得明确的限制度量来证明等均分配和非均等分配结果。对于原始合理点的翻译，也获得了类似的结果。
We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface. Using spectral methods we confirm equidistribution of these sample points for any translate when the sequence of horocycles expands within a certain polynomial range. We show that the equidistribution fails for generic translates and a slightly faster expanding rate. We also prove both equidistribution and non-equidistribution results by obtaining explicit limiting measures while allowing the sequence of horocycles to expand arbitrarily fast. Similar results are also obtained for translates of primitive rational points.
