On the Petersson norm of a Siegel-Hecke Eigenform of degree two in the Maass space.
On the Petersson norm of a Siegel-Hecke Eigenform of degree two in the Maass space.
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关于马斯空间中二阶西格尔-赫克本征型的彼得森范数。
DOI：
10.1515/crll.1985.357.96
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发表时间：
1985
期刊：
影响因子：
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通讯作者：
W. Kohnen
中科院分区：
文献类型：
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作者：
W. Kohnen
本文的目的是给出Maass空间中2次偶权k的Siegel-Hecke特征形式F的Petersson范数与权为2k-2的归一化Hecke特征形式/在SL2(Z)上对应于Saito-Kurokawa提升下的F的点的Hecke L级数Lf(S)在点S=k处的一个恒等式。这个恒等式可以很容易地从Oda[11]-[13]和Kudla[6]的工作中推导出来，当结合(由Zagier在[14]中证明)的事实时，权为k的Maass空间和某个子空间
The aim of this note is to give an identity relating the Petersson norm of a Siegel-Hecke eigenform F of degree 2 and even weight k contained in the Maass space to the value of the Hecke L-series Lf(s) at the point s = k (one unit right to the center of the critical strip) of the normalized Hecke eigenform/on SL2(Z) of weight 2k — 2, which corresponds to F under the Saito-Kurokawa lifting. This identity can easily be deduced from the work of Oda [11]—[13] and Kudla [6] when combined with the fact (proved by Zagier in [14]) that the Maass space in weight k and a certain subspace