The meromorphic continuation of the zeta function of a product of Hilbert and Picard modular surfaces over CM-fields
The meromorphic continuation of the zeta function of a product of Hilbert and Picard modular surfaces over CM-fields
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Hilbert 和 Picard 模曲面乘积的 zeta 函数在 CM 场上的亚纯延拓
DOI：
10.1016/j.jnt.2012.07.003
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发表时间：
2013
影响因子：
0.7
通讯作者：
Cristian
中科院分区：
文献类型：
--
作者：
Virdol;Cristian
在本文中，我们证明了特别是亚纯连续的zeta函数的乘积的Hilbert模曲面和Picard模曲面考虑在任何CM-域的整个复平面（见年底介绍更多的结果有关的zeta函数的亚纯连续的产品志村曲线，四元数志村曲面和Picard模曲面）。为了得到亚纯延拓，我们给出了与Hilbert模形式和Picard模曲面相关的任意有限个l-adic表示的同时势模性。
In this paper we prove in particular the meromorphic continuation to the entire complex plane of the zeta function of a product of a Hilbert modular surface and a Picard modular surface regarded over arbitrary CM-fields (see the end of the Introduction for more results regarding the meromorphic continuation of the zeta functions associated to products of Shimura curves, quaternionic Shimura surfaces and Picard modular surfaces). In order to obtain the meromorphic continuation we show the simultaneous potential modularity for an arbitrary finite number of l-adic representations associated to Hilbert modular forms and Picard modular surfaces.