论文标题
固体分布在紧凑型双曲线3个manifolds上的偏差
Bias in the distribution of holonomy on compact hyperbolic 3-manifolds
论文作者
论文摘要
环境原理定理通过其长度和全体性提供了封闭的大地测量学的渐近计数，并意味着对全体性的有效等分。我们表明，对于紧凑的双曲线3个字节上的封闭测量学的平滑计数，在次级项中存在持久偏置，该偏差由零光谱参数的数量控制。此外，我们表明，归一化的，平滑的偏置计数是根据概率分布分布的，当所有不同的非零光谱参数是线性独立的时，我们将其解释。最后，我们构建了一个无法满足这种线性独立条件的二面形式的示例。
Ambient prime geodesic theorems provide an asymptotic count of closed geodesics by their length and holonomy and imply effective equidistribution of holonomy. We show that for a smoothed count of closed geodesics on compact hyperbolic 3-manifolds, there is a persistent bias in the secondary term which is controlled by the number of zero spectral parameters. In addition, we show that a normalized, smoothed bias count is distributed according to a probability distribution, which we explicate when all distinct, non-zero spectral parameters are linearly independent. Finally, we construct an example of dihedral forms which does not satisfy this linear independence condition.
