On Siegel modular forms obtained form theta series.
On Siegel modular forms obtained form theta series.
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在西格尔模形式上从 theta 级数获得。
DOI：
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发表时间：
1984
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通讯作者：
H. Yoshida
中科院分区：
文献类型：
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作者：
H. Yoshida
在我们之前的工作[32]中，我们提出了一种构造 genus 2 的 Siegel 模形式的方法，它是 Hecke 算子的常见特征函数。结果很明确；共同的特征函数被表达为 theta 级数与附加到正定四元二次形式的球函数的线性组合。然而，一个看起来很重要的问题（参见[32]的猜想7. 6）却没有得到解决。也就是说，构造形式的不消失仅以非常弱的形式得到证明。这项工作的动机是开发一种方法来解决这个问题。
In our previous work [32], we have presented a method to construct Siegel modular forms of genus 2 which are common eigenfunctions of Hecke operators. The results were explicit; common eigenfunctions were expressed s linear combinations of theta series with spherical functions attached to positive definite quaternary quadratic forms. However a problem (cf. conjecture 7. 6 of [32]), which seems important, was left unsettled there. That is, the non-vanishing of the constructed forms was proved only in very weak form. The motivation of this work was to develop a method to attack this question.