Paramodular cusp forms
Paramodular cusp forms
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副模尖点形式
DOI：
10.1090/s0025-5718-2014-02870-6
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
D. Yuen
中科院分区：
文献类型：
--
作者：
C. Poor;D. Yuen
对于素数p<；600的准模群K(P)，我们对权为2的Siegel模尖形进行了分类。我们发现在Gritsenko提升之外的权2个Hecke本征形对应于定义在导体p的有理数域上的某些阿贝尔簇。算术分类在A.Brumer和K.Kramer的一篇文章中给出。由这些计算支持的Paramodular猜想是Shimura-Taniyama猜想的部分扩展，它与朗兰兹的哲学和吉田的工作是一致的。这些非提升Hecke本征形式与相应的阿贝尔变种$A$共享欧拉因子，并且只要$A$有有理扭转，就满足与Gritsenko提升模同余.
We classify Siegel modular cusp forms of weight two for the paramodular group K(p) for primes p< 600. We find that weight two Hecke eigenforms beyond the Gritsenko lifts correspond to certain abelian varieties defined over the rationals of conductor p. The arithmetic classification is in a companion article by A. Brumer and K. Kramer. The Paramodular Conjecture, supported by these computations and consistent with the Langlands philosophy and the work of H. Yoshida, is a partial extension to degree 2 of the Shimura-Taniyama Conjecture. These nonlift Hecke eigenforms share Euler factors with the corresponding abelian variety $A$ and satisfy congruences modulo \ell with Gritsenko lifts, whenever $A$ has rational \ell-torsion.