The spectral growth of automorphic L-functions.
The spectral growth of automorphic L-functions.
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DOI：
10.1515/crll.1992.428.139
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发表时间：
1992
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影响因子：
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通讯作者：
H. Iwaniec
中科院分区：
文献类型：
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作者：
H. Iwaniec
设w(Z)是模群Γ=sL2(Z)的权为零的Maass尖点形式，则u(Z)是双曲型拉普拉斯算子-A的本征值λ=+r，r>；0的本征函数.设u(Z)也是具有特征值λ(η)的所有黑克算子Tn的特征函数，且u(x+iy)在x中为偶数或奇数，即u(-z)-δu(Z)且δ=L，-L。与u(Z)相关的Hecke的Zeta函数由级数给出
Let w (z) be a Maass cusp form of weight zero for the modular group Γ = SL2(Z), thus u (z) is an eigenfunction of the hyperbolic Laplace operator —A with eigen value λ = + r, r > 0. Suppose that u (z) is also an eigenfunction of all the Hecke operators Tn with eigenvalues λ(η) respectively and that u(x + iy) is either even or odd in x, i.e. u( — z) — δ u (z) with δ = l, — l respectively. The zeta-function of Hecke associated with u (z) is given by the series