GL$(n)$上尖形扭转等价的约束

Pub Date : 2019-06-03 DOI:10.7169/FACM/1913

D. Ramakrishnan, Liyang Yang

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引用次数: 2

摘要

本文回答并概括了Kaisa Matomaki的一个问题。我们给出了两个逆自同构表示 $\pi_1$ 和 $\pi_2$ 的 $GL_n$ 在一个数字域上 $F$ 各自导体的 $N_1,$ $N_2,$ 每个角色 $\chi$ 这样 $\pi_1\otimes\chi\simeq\pi_2$ 导体 $Q,$ 满足界: $Q^n\mid N_1N_2.$ 如果在每一个有限的位置 $v,$ $\pi_{1,v}$ 无论什么时候它的分支都是离散级数 $Q^n$ 除以最小公倍数 $[N_1, N_2].$

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A constraint for twist equivalence of cusp forms on GL$(n)$

This note answers, and generalizes, a question of Kaisa Matomaki. We show that give two cuspidal automorphic representations $\pi_1$ and $\pi_2$ of $GL_n$ over a number field $F$ of respective conductor $N_1,$ $N_2,$ every character $\chi$ such that $\pi_1\otimes\chi\simeq\pi_2$ of conductor $Q,$ satisfies the bound: $Q^n\mid N_1N_2.$ If at every finite place $v,$ $\pi_{1,v}$ is a discrete series whenever it is ramified, then $Q^n$ divides the least common multiple $[N_1, N_2].$

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