COMPUTATIONS OF SPACES OF PARAMODULAR FORMS OF GENERAL LEVEL
COMPUTATIONS OF SPACES OF PARAMODULAR FORMS OF GENERAL LEVEL
复制标题
一般能级的拟调形式空间的计算
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
D. Yuen
中科院分区：
文献类型：
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作者：
Jeffery Breeding;C. Poor;D. Yuen
本文给出了确定二次仿模尖点型的Fourier- Jacobi系数个数的上界。副模群的水平N始终是完全一般的。此外，Jacobi尖点形式的空间是由Gritsenko，Skoruppa和Zagier的theta块的理论来张成的。我们将这两种方法联合收割机结合起来，严格地计算了仿模尖点型空间，并在许多低水平的情况下验证了Brumer和克雷默的仿模猜想.证明依赖于每个paramodular群中的积分元素的子群的零维尖点的详细描述。
This article gives upper bounds on the number of Fourier- Jacobi coecients that determine a paramodular cusp form in degree two. The level N of the paramodular group is completely general throughout. Additionally, spaces of Jacobi cusp forms are spanned by using the theory of theta blocks due to Gritsenko, Skoruppa and Zagier. We combine these two techniques to rigorously compute spaces of paramodular cusp forms and to verify the Paramodular Conjecture of Brumer and Kramer in many cases of low level. The proofs rely on a detailed description of the zero dimensional cusps for the subgroup of integral elements in each paramodular group.