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

Dinakar Ramakrishnan; Liyang Yang

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arXiv · 1906.01047

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

Dinakar Ramakrishnan·Liyang Yang

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Abstract

This Note answers, and generalizes, a question of Kaisa Matom\"aki. We show that give two cuspidal automorphic representations $\pi_1$ and $\pi_2$ of $GL_n$ over a number field $F$ of respective conductors $N_1,$ $N_2,$ 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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Dinakar Ramakrishnan, Liyang Yang. 2019-06-03. A constraint for twist equivalence of cusp forms on GL$(n)$. https://arxiv.org/abs/1906.01047

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