Isolating Rankin-Selberg lifts

Getz, Jayce; Klassen, Jamie

doi:10.1090/proc/12389

Isolating Rankin-Selberg lifts
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by Jayce R. Getz and Jamie Klassen PDF

Proc. Amer. Math. Soc. 143 (2015), 3319-3329 Request permission

Abstract:

Let $F$ be a number field and let $\pi$ be a cuspidal unitary automorphic representation of $\mathrm {GL}_{mn}(\mathbb {A}_F)$ where $m$ and $n$ are integers greater than one. We propose a conjecturally necessary condition for $\pi$ to be a Rankin-Selberg transfer of an automorphic representation of $\mathrm {GL}_m \times \mathrm {GL}_n(\mathbb {A}_F)$. As evidence for the conjecture we prove the corresponding statement about automorphic $L$-parameters.

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