Periods, poles of L-functions and symplectic-orthogonal theta lifts.
Periods, poles of L-functions and symplectic-orthogonal theta lifts.
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DOI：
10.1515/crll.1997.487.85
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
D. Ginzburg;S. Rallis;D. Soudry
中科院分区：
文献类型：
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作者：
D. Ginzburg;S. Rallis;D. Soudry
作为其正则化的Siegel-Weil公式的应用，Kudla和Rallis在[K.R.]，定理7.2.6中证明了：对于Sp2n(A)的一个不可约的、自同构的尖角表示π，标准(部分)L函数L(n，S)的唯一可能的极点是简单的，且出现在点L，2，.。-L·LΛ如果L(n，S)在给定点有一个极点，则π到适当的正交群的提升力不为零。正交群对应于一个二次型，其判别性质是平凡的。例如，在S=L时，二次型是2/7个变量。本文将注意力仅限于一般的π，即具有非平凡惠特克系数的极，并证明了·L(n，S)唯一可能的极点在S=L，
As an application of their regularized Siegel-Weil formula, Kudla and Rallis prove in [K.R.], Theorem 7.2.6, that for an irreducible, automorphic, cuspidal representation π of Sp2n(A), the only possible poles of the Standard (partial) L-function L(n,s) are simple and occur at the points < l, 2,.. . , -l· l Λ If L(n,s) has a pole at a given point, then the theta lift of π, to an appropriate orthogonal group, is nonzero. The orthogonal group corresponds to a quadratic form, whose discriminant character is trivial. For example, at s = l, the quadratic form is in 2/7 variables. In this paper, we restrict attention to generic π only, i.e. those with nontrivial Whittaker coefficients, and then we show that • the only possible pole of L(n,s) is at s = l,