关于Schottky曲面上Eisenstein级数的节线
On the nodal lines of Eisenstein series on Schottky surfaces
摘要：
在极限集的豪斯多夫维数小于小于1/2的凸余紧双曲曲面上，研究了Eisenstein级数的高能行为. Eisenstein级数是双曲拉普拉斯算子的非L^2特征函数，它将连续谱参数化。我们证明了一个等距分布的结果，限制测地线段，并使用它来获得最佳的下限和上界的交叉点的数目与一个固定的测地线段的频率趋于无穷大。节点域个数的上界也被导出。
英文摘要：
On convex co-compact hyperbolic surfaces with Hausdorff dimension of the limit set less than 1/2, we investigate high energy behaviour of Eisenstein Series. Eisenstein Series are non-L^2 eigenfunctions of the hyperbolic Laplacian which parametrize the continous spectrum. We prove an equidistribution result for restrictions to geodesics segments and use it to obtain optimal lower and upper bounds for the number of intersections of nodal lines with a fixed geodesic segment as the frequency goes to infinity. Upper bounds on the number of nodal domains are also derived.
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