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Ramanujan duals and automorphic spectrum

Marc Burger·Jian-Shu Li·Peter Sarnak
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Abstract

We introduce the notion of the automorphic dual of a matrix algebraic group defined over $Q$. This is the part of the unitary dual that corresponds to arithmetic spectrum. Basic functorial properties of this set are derived and used both to deduce arithmetic vanishing theorems of ``Ramanujan'' type as well as to give a new construction of automorphic forms.

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Marc Burger, Jian-Shu Li, Peter Sarnak. 1992-04-01. Ramanujan duals and automorphic spectrum. https://arxiv.org/abs/math/9204229

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