论文标题
Heegner点的双曲线角度
Hyperbolic angles from Heegner points
论文作者
论文摘要
我们研究以第一级赫德纳点为中心的双曲线圆圈的晶格点。我们的主要结果是，在密度的一个子集中，半径趋向于无穷大，在单位圆上等分分布的角度。为了证明这一点，我们在相关字段中建立了晶格点和代数整数之间的联系，具有特殊形式的规范并满足了一致性条件。作为此的副产品，我们获得了经典双曲圆问题的明确公式，作为换移的卷积总和，该函数计算了具有给定标准的代数整数数量。一路上，我们还证明了用于移动的B数字的下限，这是通过筛子方法完成的。
We study lattice points on hyperbolic circles centred at Heegner points of class number one. Our main result is that, on a density one subset of radii tending to infinity, the angles of such points equidistribute on the unit circle. To prove this, we establish a connection between lattice points and algebraic integers in the associated field having norm of a special form and satisfying a congruence condition. As a by-product of this, we obtain an explicit formulation of the classical hyperbolic circle problem as a shifted convolution sum for the function that counts the number of algebraic integers with given norm. Along the way, we also prove a lower bound for shifted B-numbers, which is done by sieve methods.
