Ramanujan Duals and Automorphic Spectrum

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


Publications referenced by this paper.
Showing 1-10 of 21 references

Mennicke, Poincaré series, Kloosterman sums, and eigenvalues of the Laplacianfor congruence groups acting on hyperbolic spaces

  • J. Elstrodt, T. F. Grunewald
  • Invent. Math
  • 1990

A description of the discrete series for semisimple symmetric spaces

  • T. Oshima
  • Adv . Stud . Pure Math .
  • 1989

Discrete subgroups of semi-simple Lie groups

  • G Margulis
  • Ergeb. Math. Grenzeb. (3), vol. 17 Springer…
  • 1989
1 Excerpt

Poincaré series for SO(n

  • J. S. Li, I. Piatetsky-Shapiro, P. Sarnak
  • Proc. Indian Acad. Sei
  • 1987

A description of the discrete series for semi-simple symmetric spaces, Adv

  • T. Matsuki, T. Oshima
  • Stud. Pure Math
  • 1984

Barbasch, The unitary dual of real rank one groups

  • D. BB M.W. Baldoni-Silva
  • Invent Math
  • 1983

Piatetski-Shapiro, Some examples of automorphic forms on Sp(4)

  • I. R. Howe
  • Duke Math. J
  • 1983

Geometric construction of cohomology for arithmetic groups I

  • J. Millson, M. Raghunathan
  • Proc. Indian Acad. Sei. Math. Sei
  • 1981

Almost L 2matrix coefficients

  • U. Haagerup, R. Howe
  • Ann . of Math . Stud .
  • 1980

Continuous cohomology, discrete subgroups and representations of reductive groups

  • BW A. Borel, N. Wallach
  • Ann. of Math. Stud
  • 1980

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