Jacquet–Langlands correspondence

In mathematics, the Jacquet–Langlands correspondence is a correspondence between automorphic forms on GL2 and its twisted forms, proved by Jacquet and Langlands (1970, section 16) in their book Automorphic Forms on GL(2) using the Selberg trace formula. It was one of the first examples of the Langlands philosophy that maps between L-groups should induce maps between automorphic representations.

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