Abstract:We prove, under certain assumptions, algebraicity of the ratio $L(m, \Pi \times \chi)/L(m, \Pi \times \chi')$, where $\Pi$ is a cuspidal automorphic cohomological unitary representation of $\mathrm{GL}_n(\mathbb{A}_\mathbb{Q})$, and $\chi$, $\chi'$ are finite order Hecke characters such that $\chi_{\infty} = \chi'_{\infty} = \mathrm{sgn}^{r}$, and $m, r$ are specific positive integers which depends only on $\Pi_{\infty}$. The methods in this article are a generalization of those in the work of Mahnkopf [Cohomology of arithmetic groups, parabolic subgroups and the special values of $L$-functions of GL(n), J. Inst. Math. Jussieu, 4 (2005)].
From: Ankit Rai [view email]
[v1]
Sat, 23 Mar 2024 10:51:18 UTC (27 KB)
[v2]
Sun, 8 Sep 2024 16:35:38 UTC (30 KB)
[v3]
Fri, 12 Jun 2026 11:03:16 UTC (29 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。