Periods of automorphic forms over reductive subgroups
Periods of automorphic forms over reductive subgroups
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还原子群上的自守形式周期
DOI：
10.24033/asens.2493
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Michał Zydor
中科院分区：
文献类型：
--
作者：
Michał Zydor
给出了任意约化子群$G‘\子集G$上群$G$上自同构形式的周期积分的正则化过程.作为结果，我们得到了一个显式的$G‘(\mathbb{A})$-不变泛函，它的指数避开了某些指定的超平面。给出了自同构型的周期积分按指数收敛的充要条件。
We present a regularization procedure of period integrals of automorphic forms on a group $G$ over an arbitrary reductive subgroup $G' \subset G$. As a consequence we obtain an explicit $G'(\mathbb{A})$-invariant functional on the space of automorphic forms on $G$ whose exponents avoid certain prescribed hyperplanes. We also provide a necessary and sufficient condition for convergence of period integrals of automorphic forms in terms of their exponents.