论文标题
残留分布，迭代残留物和球形自身谱
Residue distributions, iterated residues, and the spherical automorphic spectrum
论文作者
论文摘要
让$ g $为一个数字字段$ f $的拆分还原组。我们考虑通过langlands启动的经典方法来考虑$ [T，\ Mathcal {o}（1）] $支持的两个$ k $ -spherical pseudo eisenstein系列的$ g $。我们表明，仅由于完成的Dedekind Zeta函数$λ_F$的杆子而导致的相互交织运算符的奇异性有助于频谱，而由$λ_f$的零引起的奇异性并不造成任何由于必要的轮廓而产生的迭代残留物。 在同伴论文[dmho]中，我们使用此结果来明确确定$ l^2（g（f）\ backslash g（\ mathbb {a} _f），ξ）^k _ {[t，\ mathcal {o} {o}（1）]} $的频谱分配。
Let $G$ be a split reductive group over a number field $F$. We consider the computation of the inner product of two $K$-spherical pseudo Eisenstein series of $G$ supported in $[T,\mathcal{O}(1)]$ by means of residues, following a classical approach initiated by Langlands. We show that only the singularities of the intertwining operators due to the poles of the completed Dedekind zeta function $Λ_F$ contribute to the spectrum, while the singularities caused by the zeroes of $Λ_F$ do not contribute to any of the iterated residues which arise as a result of the necessary contour shifts. In the companion paper [DMHO] we use this result to explicitly determine the spectral measure of $L^2(G(F)\backslash G(\mathbb{A}_F),ξ)^K_{[T,\mathcal{O}(1)]}$ by a comparison of the iterated residues with the residue distributions of [HO1].
