The completed standard L-function of modular forms on $$G_2$$
The completed standard L-function of modular forms on $$G_2$$
复制标题
$$G_2$$ 上已完成的模块化形式的标准 L 函数
DOI：
10.1007/s00209-022-03067-8
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发表时间：
2022
影响因子：
0.8
通讯作者：
Roy, Manami
中科院分区：
文献类型：
--
作者：
Çiçek, Fatma;Davidoff, Giuliana;Dijols, Sarah;Hammonds, Trajan;Pollack, Aaron;Roy, Manami
本文的目的是对的某些非一般尖角自同构表示的标准L-函数提供一个完整而精细的研究。对于对应于一阶偶权模形式的尖点自同构表示，我们显式定义了完备的标准L-函数。假设的某个傅立叶系数不为零，我们证明了函数方程。我们的证明是通过仔细分析一个Rankin-Selberg积分来进行的，该积分源于Gurevich和西格尔早期的工作。
The goal of this paper is to provide a complete and refined study of the standardL-functionsfor certain non-generic cuspidal automorphic representationsof. For a cuspidal automorphic representationofthat corresponds to a modular formof level one and of even weight on, we explicitly define the completed standardL-function,. Assuming that a certain Fourier coefficient ofis nonzero, we prove the functional equation. Our proof proceeds via a careful analysis of a Rankin-Selberg integral that is due to an earlier work of Gurevich and Segal.