Ramanujan duals and automorphic spectrum

M. Burger; J. S. Li; P. Sarnak

doi:10.1090/S0273-0979-1992-00267-7

Ramanujan duals and automorphic spectrum

M. Burger, J. S. Li, P. Sarnak

Mathematics

Research output: Contribution to journal › Comment/debate › peer-review

39 Scopus citations

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.

Original language	English (US)
Pages (from-to)	253-257
Number of pages	5
Journal	Bulletin of the American Mathematical Society
Volume	26
Issue number	2
DOIs	https://doi.org/10.1090/S0273-0979-1992-00267-7
State	Published - Apr 1992

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0273-0979-1992-00267-7

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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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AU - Sarnak, P.

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N2 - 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.

AB - 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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U2 - 10.1090/S0273-0979-1992-00267-7

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M3 - Comment/debate

AN - SCOPUS:84967787237

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EP - 257

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

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Ramanujan duals and automorphic spectrum

Abstract

All Science Journal Classification (ASJC) codes

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