Level-raising for automorphic forms on 𝐺𝐿_{𝑛}

Karnataki, Aditya

doi:10.1090/tran/8439

Level-raising for automorphic forms on $GL_n$
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Trans. Amer. Math. Soc. 374 (2021), 8547-8572 Request permission

Abstract:

Let $E$ be a CM number field and $F$ its maximal real subfield. We prove a level-raising result for regular algebraic conjugate self-dual automorphic representations of $GL_{n}(\mathbb {A}_E)$. This generalizes previously known results of Thorne [Forum Math. Sigma 2 (2014)] by removing certain hypotheses occurring in that work. In particular, the level-raising prime $p$ is allowed to be unramified as opposed to inert in $F$, the field $E/F$ is not assumed to be everywhere unramified, and the field $E$ is allowed to be a general CM field.

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