论文标题
在当地的$ l^2 $ bind of Eisenstein系列
On the local $L^2$-Bound of the Eisenstein Series
论文作者
论文摘要
我们在其参数方面研究了元素艾森斯坦系列的局部$ l^2 $ norms在数量字段上的生长。对于一大批还原组，我们得出了平均绑定的A \ emph {poly-logarithmic}。该方法是基于亚瑟（Arthur）对痕量公式的光谱侧的发展，以及Finis，Lapid和Müller的思想。作为我们方法的应用，我们证明了$ \ mathrm {sl} _n（\ Mathbb {z}/q \ Mathbb {z}）$的最佳提升属性，用于无方形$ q $，以及sarnak--- xue计数属性的主要祝贺属性$ \ m m i} $ sl} $ {无方级。这是Assing的最新结果 - blomer无条件。
We study the growth of the local $L^2$-norms of the unitary Eisenstein series for reductive groups over number fields, in terms of their parameters. We derive a \emph{poly-logarithmic} bound on an average, for a large class of reductive groups. The method is based on Arthur's development of the spectral side of the trace formula, and ideas of Finis, Lapid, and Müller. As applications of our method, we prove the optimal lifting property for $\mathrm{SL}_n(\mathbb{Z}/q\mathbb{Z})$ for square-free $q$, as well as the Sarnak--Xue counting property for the principal congruence subgroup of $\mathrm{SL}_n(\mathbb{Z})$ of square-free level. This makes the recent results of Assing--Blomer unconditional.
