References
[A1]J. Arthur, The Selberg trace formula for groups ofF-rank one, Ann. of Math. 100 (1974), 326–385.
[A2]J. Arthur, Eisenstein series and the trace formula, Proc. of the Symp. in Pure Math. 33, Providence 1979, 253–274.
[CS]P. Cohen, P. Sarnak, Discrete groups and harmonic analysis, (manuscript).
[D]H. Donnely, On the Cuspidal Spectrum for finite volume symmetric spaces, J. Diff. Geom. 17 (1982), 239–253.
[E1]I. Efrat, The Selberg Trace Formula For PSL n2 (ℝ), Memoirs of AMS 65 (1987).
[E2]I. Efrat, On the Automorphic Forms of a Noncongruence subgroup, Michigan M.J. 34, (1987), 217–226.
[E3]I. Efrat, Eisenstein series and Cartan groups, Illinois J. of Math. 31, 3 (1987), 428–437.
[ES]I. Efrat, P. Sarnak, The determinant of the Eisenstein matrix, Trans. Amer. Math. Soc. 290 (1985), 815–824.
[F]L. Faddeev, Expansion in eigenfunctions of the Laplacian, Trans. Moscow Math. Soc. 17 (1976), 357–386.
[G]L. Goldstein, Analytic Number Theory, Prentice-Hall, 1971.
[GPR]S. Gelbart, I. Piatetski-Shapiro, S. Rallis, Explicit Constructions of AutomorphicL-functions, Springer Lectue Notes in Mathematics 1254 (1987).
[H]Harish-Chandra, Automorphic Forms on Semi-simple Lie Groups, Springer Lecture Notes in Mathematics 62 (1968).
[He]D. Hejhal, The Selberg Trace Formula for PSL2(ℝ), Springer Lecture Notes in Mathematics 548, 1001 (1976, 1983).
[Hu]M. Huxley, Scattering Matrix, in “Modular Forms and Automorphic Functions”, ed. R. Rankin, Halsted Press, 1986.
[KP]D. Kazhdan, S. Patterson, Metaplectic forms, I.H.E.S. 59 (1984).
[K]T. Kubota, On automorphic forms and the reciprocity law, Kyoto University, Japan (1969).
[L]R. Langlands, On the Functional Equation Satisfied by Eisenstein Series”, Springer Lecture Notes in Mathematics 544 (1976).
[La]K. Lai, Tamagawa number of reductive algebraic groups, Comp. Mat. 41 (1980), 153–188.
[LP]P. Lax P., R. Philips, Scattering Theory for Automorphic Functions, Math. Studies 87, Princeton, 1976.
[P]S. Patterson, A cubic analogue of the theta series, J. fur R.U.A. Math. 296 (1977), 125–161.
[S1]P. Sarnak, On Cusp Forms 1, Contemp. Math. 53 (1986), 393–397.
[S2]P. Sarnak, On Cusp Forms 2, in “Festschrift in Honor of I.I. Piatetski-Shapiro on his Sixtieth Birtday”, IMCP 2, Weizmann Science Press (1990), 237–250.
[Sb]A. Selberger, Introduction to Harmonic Analysis on Reductivep-adic Group, Math. Notes 23, Princeton, 1979.
[Sl]A. Selberg, Harmonic analysis and discontinuous groups, J. Indian Math. Soc. 20 (1956), 47–87.
[V]A. Venkov, Expansion in Automorphic Eigenfunctions of the Laplace-Beltrami operator, Proc. Steklov Inst. Math. 125 (1975), 1–48.
[VZ]A. Venkov, P. Zograf, On analogues of the Artin factorisation formulas, Soviet Math. Dokl. 24, 1 (1981), 94–96.
[T]J. Tits, Classification of algebraic semisimple groups, Proc. Sympos. Pure Math. 9, Amer. Math. Soc. Providence (1966), 33–62.
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Reznikov, A. Eisenstein matrix and existence of cusp forms in rank one symmetric spaces. Geometric and Functional Analysis 3, 79–105 (1993). https://doi.org/10.1007/BF01895514
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DOI: https://doi.org/10.1007/BF01895514