Determination of cusp forms by central values of Rankin–Selberg L-functions*
Determination of cusp forms by central values of Rankin–Selberg L-functions*
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DOI：
10.1007/s10986-011-9147-z
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发表时间：
2011-11
影响因子：
0.4
通讯作者：
Qinghua Pi
中科院分区：
文献类型：
--
作者：
Qinghua Pi
设f为weightkfor的固定全纯赫克本征尖点形式，设为Hecke-Maass尖点形式的标准正交基。我们证明了Rankin-SelbergL-函数satasujruns 的扭曲一阶矩的渐近公式。由此可见，f 由 Rankin-SelbergL 函数族的中心值唯一确定。
Letfbe a fixed holomorphic Hecke eigen cusp form of weightkfor, and letbe an orthonormal basis of Hecke–Maass cusp forms for. We prove an asymptotic formula for the twisted first moment of the Rankin–SelbergL-functionsatasujruns over. It follows thatfis uniquely determined by the central values of the family of Rankin–SelbergL-functions.