Proof of R. Salvati Manni and J. Top's conjectures on Siegel modular forms and Abelian surfaces
Proof of R. Salvati Manni and J. Top's conjectures on Siegel modular forms and Abelian surfaces
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R. Salvati Manni 和 J. Top 关于西格尔模形式和阿贝尔曲面猜想的证明
DOI：
10.1353/ajm.2006.0008
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发表时间：
2006
影响因子：
1.7
通讯作者：
T. Okazaki
中科院分区：
文献类型：
--
作者：
T. Okazaki
本文给出了R. Salvati Manni和J. Top的定理，它们包含在“Cusp forms of weight 2 for the group Γ（4，8），Amer. J. Math . 115（1993），455-486.“其中一个论点声称，对应于在超椭圆曲线y 2 = x 5 - x的[inline-graphic xmlns：xlink=”http://www.w3.org/1999/xlink“xlink：href=“01 i”/]上定义的雅可比簇的Hasse-Weil zeta函数等于次数为2且权重为2的Siegel尖点形式Θ的Andrianov L -函数，其是Igusa θ常数的四个乘积。将Θ看作是由一对椭圆模形式通过Yoshida提升得到的函数，证明了该猜想.
This paper gives complete proofs of R. Salvati Manni and J. Top's conjectures which are contained in the paper, "Cusp forms of weight 2 for the group Γ(4, 8), Amer. J. Math . 115 (1993), 455-486." One of the conjectures claims that the Hasse-Weil zeta function corresponding to the Jacobian variety defined over [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] of the hyper-elliptic curve y 2 = x 5 - x equals the Andrianov L -function of Siegel cusp form Θ of degree 2 and weight 2 which is four products of the Igusa theta constants. Regarding the Θ as a function obtained by the Yoshida lifting from a pair of elliptic modular forms, we prove the conjecture.
影响因子：
3.1
作者：
J. Milne
通讯作者：
J. Milne