On special Bessel periods and the Gross-Prasad conjecture for SO(2n+1)xSO(2)
On special Bessel periods and the Gross-Prasad conjecture for SO(2n+1)xSO(2)
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关于特殊贝塞尔周期和 SO(2n 1)xSO(2) 的 Gross-Prasad 猜想
DOI：
10.1007/s00208-016-1440-z
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发表时间：
2017
影响因子：
1.4
通讯作者：
Masaaki Furusawa and Kazuki Morimoto
中科院分区：
文献类型：
--
作者：
Benoit Collins;Sho Matsumoto;Jonathan Novak;Masaaki Furusawa and Kazuki Morimoto
本文研究了全局Gross-Prasad猜想的一个实例。我们的主要结果证明，如果奇维特殊正交群的不可约逆自同构表示，其局部分量在某有限位置w是一般的，允许基域F上对应二次扩展E的特殊贝塞尔模型，则中心l值不消失。作为一个应用，我们得到了与二阶全模全纯Siegel尖形（Hecke特征形）相关的特殊贝塞尔周期的不灭性与对应的中心l值的不灭性的等价性，而E是的虚二次扩展。
In this paper we investigate one instance of the global Gross-Prasad conjecture. Our main result proves that if an irreducible cuspidal automorphic representationof an odd dimensional special orthogonal group, whose local componentat some finite place w is generic, admits the special Bessel model corresponding to a quadratic extension E over a base field F, then the central L-valuedoes not vanish. Heredenotes the quadratic character ofcorresponding to E. As an application, we obtain the equivalence between the non-vanishing of the special Bessel period and that of the corresponding central L-value whenis associated to a full modular holomorphic Siegel cusp form of degree two, which is a Hecke eigenform, and E is an imaginary quadratic extension of.