论文标题
反DE保姆的广义庞加莱系列的线性独立性3-manifolds
Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds
论文作者
论文摘要
令$γ$为一个离散的组，在三维抗DE保姆空间上正确地作用，并等法地行动$ \ mathrm {ads}^{3} $，以及$ \ square $ laplacian，是二阶多粒子差异操作员。我们研究了一个普遍的Poincar家族的线性独立性＆＃233;由Kassel-Kobayashi提出的系列[Adv。数学。 287（2016），123-236，arxiv：1209.4075]，由$ \ m atrm {ads}^{3} $上的某些特征函数的$γ$ - 平均定义。我们证明，$ l^{2} $的多重性 - $γ\ backslash \ mathrm {ads}^{3} $在$γ$中是$γ$时，$γ\ backslash \ mathrm {ads}^{3} $在$γ$中是无绑定的。此外，我们证明了稳定的$ l^{2} $的多样性 - 紧凑型抗De保姆3个manifolds的特征值是无限的。
Let $Γ$ be a discrete group acting properly discontinuously and isometrically on the three-dimensional anti-de Sitter space $\mathrm{AdS}^{3}$, and $\square$ the Laplacian which is a second-order hyperbolic differential operator. We study linear independence of a family of generalized Poincaré series introduced by Kassel-Kobayashi [Adv. Math. 287 (2016), 123-236, arXiv:1209.4075], which are defined by the $Γ$-average of certain eigenfunctions on $\mathrm{AdS}^{3}$. We prove that the multiplicities of $L^{2}$-eigenvalues of the hyperbolic Laplacian $\square$ on $Γ\backslash\mathrm{AdS}^{3}$ are unbounded when $Γ$ is finitely generated. Moreover, we prove that the multiplicities of stable $L^{2}$-eigenvalues for compact anti-de Sitter 3-manifolds are unbounded.
