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# Ramanujan Duals and Automorphic Spectrum

@inproceedings{Burger1992RamanujanDA, title={Ramanujan Duals and Automorphic Spectrum}, author={Marc J. C. Burger and Jin Song Li and Peter Sarnak}, year={1992} }

- Published 1992

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 funcional 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. Let G be a semisimple linear algebraic group defined over Q. In the arithmetic theory of automorphic forms the lattice Y — G(Z) and its… CONTINUE READING