论文标题
在兰兰兹的光谱定理上
On the spectral Theorem of Langlands
论文作者
论文摘要
我们表明，由Eisenstein系列的波数据包生成的$ L^2（g（f）\ Backslash G（\ a））$的希尔伯特子空间是由离散系列构建的。加上Lapid \ cite {l1}的工作，它基于伯恩斯坦和拉皮德\ cite {bl}在Eisenstein系列的Meromorphic Conteriation上的工作，实现了Langlands的光谱定理的证明。我不得不说我无法完成较早版本的证明。取而代之的是，我在紧凑型集合上使用截断，就像亚瑟所做的那样，在\ cite {alt}中证明了本地跟踪公式。
We show that the Hilbert subspace of $L^2(G(F)\backslash G(\A))$ generated by wave packets of Eisenstein series built from discrete series is the whole space. Together with the work of Lapid \cite{L1}, it achieves a proof of the spectral theorem of Langlands based on the work of Bernstein and Lapid \cite{BL} on the meromorphic continuation of Eisenstein series. I have to say that I was unable to complete the proof of an earlier version. Instead, I use truncation on compact sets, as Arthur did to prove the Local Trace Formula in \cite{Alt}.
