Congruence Between a Siegel and an Elliptic Modular Form
Congruence Between a Siegel and an Elliptic Modular Form
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西格尔模与椭圆模形式之间的一致性
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Harder
中科院分区：
文献类型：
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作者：
G. Harder
2002/2003冬季学期是我从大学退休前的最后一个学期。碰巧我是座谈会的主席，原定于2月7日举行的演讲者不得不取消他的访问。几乎在同一时间，我发现了一个非常普遍的猜想的数值支持，该猜想将L函数的某些特定值的可除性与模形式之间的同余联系联系起来。我多年来一直在思考这种关系，但我从来不知道如何才能找到实验证据。但在2003年初，C.Faber和G.van der Geer编写了一个程序，生成了一些特殊的Siegel模形式上的Hecke算子的本征值列表。在悬而未决的几天之后，我们可以将他们的列表与我的椭圆模形式的特征值列表进行比较，并验证我们的例子中的同余。
The winter semester 2002/2003 was the last semester before my retirement from the university. It also happened that I was the chairman of the Colloquium and the speaker foreseen for February 7 had to cancel his visit. At about the same time I found some numerical support for a very general conjecture relating divisibilities of certain special values of L-functions to congruences between modular forms. I have been thinking about this kind of relationship for many years, but I never had any idea how one could find experimental evidence. But in the early 2003 C. Faber and G. van der Geer had written a program that produced lists of eigenvalues of Hecke operators on some special Siegel modular forms. After a few days of suspense we could compare their list with my list of eigenvalues of elliptic modular forms and verify the congruence in our examples.