Local newforms and formal exterior square L-functions
Local newforms and formal exterior square L-functions
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局部新形式和正式的外部方形 L 函数
DOI：
10.1142/s179304211350070x
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发表时间：
2013
影响因子：
0.7
通讯作者：
Takuya Yamauchi
中科院分区：
文献类型：
--
作者：
Michitaka Miyauchi;Takuya Yamauchi
设F是特征为零的非阿基米德局部域。Jacquet和Shalika在Gln(F)的酉不可约一般表示π上附加了一族Zeta积分族。在本文中，我们证明了当π的惠特克函数与一种新的形式相联系时，雅克-沙里卡积分达到了某一维特函数，即所谓的形式平方L函数。通过伽罗华侧的考虑，对于某些主级数表示，形式外方L函数等于外方L函数。
Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GLn(F). In this paper, we show that the Jacquet–Shalika integral attains a certain L-function, the so-called formal exterior square L-function, when the Whittaker function is associated to a newform for π. By considerations on the Galois side, formal exterior square L-functions are equal to exterior square L-functions for some principal series representations.