论文标题
双曲线表面的Abelian覆盖物：光谱的等分分配和无限量混合肌周期流量
Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows
论文作者
论文摘要
我们认为紧凑的双曲线表面的Abelian覆盖物。我们建立了在$ \ mathbb {z}^d $ - covers上的烟节流相关性的渐近扩展，从而证明了krickeberg混合的强烈形式。我们还证明，在任何有限的Abelian覆盖序列上，频谱量约$ 0 $的Casimir运营商均弱化为绝对连续的度量。
We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on $\mathbb{Z}^d$-covers, thus proving a strong form of Krickeberg mixing. We also prove that the spectral measures around $0$ of the Casimir operators on any increasing sequence of finite Abelian covers converge weakly to an absolutely continuous measure.
