Hecke eigenvalues and relations for Siegel Eisenstein series of arbitrary degree, level, and character
Hecke eigenvalues and relations for Siegel Eisenstein series of arbitrary degree, level, and character
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任意阶数、水平和特征的 Siegel Eisenstein 级数的 Hecke 特征值和关系
DOI：
10.1142/s179304211750021x
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
L. Walling
中科院分区：
文献类型：
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作者：
L. Walling
我们评估了Hecke算子在任意次数、水平和性质的Siegel Eisenstein级数上的作用。对于无平方能级，我们同时将空间关于所有的Hecke算子对角化，显式地计算本征值，并得到多个一的结果。对于任意能级，我们同时对角化与素数有关的Hecke算子而不划分能级，再次显式计算本征值。
We evaluate the action of Hecke operators on Siegel Eisenstein series of arbitrary degree, level and character. For square-free level, we simultaneously diagonalize the space with respect to all the Hecke operators, computing the eigenvalues explicitly, and obtain a multiplicity-one result. For arbitrary level, we simultaneously diagonalize the space with respect to the Hecke operators attached to primes not dividing the level, again computing the eigenvalues explicitly.