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References
[Bassr] Barnes, E.W.: The theory of the G-function. Q.J. Math.31, 264–314 (1900)
[B1] Bateman, H.: Tables of integral transforms, vol. I. New York Toronto London: McGraw-Hill 1954
[B2] Bateman, H.: Tables of integral transforms, vol. II New York Toronto London: McGraw-Hill 1954
[B3] Bateman, H.: Higher transcendental functions, vol. I. New York Toronto London: McGraw-Hill 1953
[Bau] Baumgärtel, H.: Analytic Perturbation Theory of Matrices and Operators. Berlin: Akademie-Verlag 1984
[Bér] Bérard, P.: Transplantation et isospectralité I. (Preprint 1990)
[Be] Bers, L.: A remark on Mumford's compactness theorem. Isr. J. Math.12, 400–407 (1972)
[Bo] Boas, R.P.: Entire Functions. New York: Academic Press 1954
[CG] Cheeger, J., Gromov, M.: On the characteristic numbers of complete manifolds of bounded geometry and finite volume. In: Chavel I., Farkas, H.M. (eds.) Differential Geometry and Complex Analysis, pp. 115–154. Berlin Heidelberg New York: Springer 1985
[Ch] Chernoff, P.R.: Essential self-adjointness of powers of generators of hyperbolic equations. J. Funct. Anal.12, 401–414 (1973)
[C1] Colin de Verdiere, Y.: Une nouvelle démonstration du prolongement méromorphe de séries d'Eisenstein. C.R. Acad. Sci. Paris, Sér. I293, 361–363 (1981)
[C2] Colin de Verdiere, Y.: Pseudo-Laplacians II. Ann. Inst. Fourier33, 87–113 (1983)
[DM] Davies, E.B., Mandouvalos, N.: Heat kernel bounds on manifolds with cusps. J. Funct. Analysis75, 311–322 (1987)
[DT] Deift, P., Trubowitz, E.: Inverse scattering on the line. Commun. Pure Appl. Math.32, 121–251 (1979)
[E1] Efrat, I.: Determinants of Laplacians on surfaces of finite volume. Commun. Math. Phys.119, 443–451 (1988)
[E2] Efrat, I.: Erratum: Determinants of Laplacians on surfaces of finite volume. Commun. Math. Phys.138, 607 (1991)
[FK] Fricke, R., Klein, F.: Vorlesungen über die Theorie der automorphen Funktionen, vol. I. Leipzig: Teubner 1896/1912
[G] Gelfand, I.M.: Automorphic functions and the theory of representations. In: Proc. Int. Cong. Math., Stockholm, pp. 74–85. Diursholm: Institute Mittag-Leffler 1963
[Ha] Hayman, W.K.: Meromorphic functions. Oxford: Clarendon, Oxford University Press 1964
[H1] Hejhal, D.A.: The Selberg trace formula and the Riemann zeta function. Duke Math. J.43, 441–482 (1976)
[H2] Hejhal, D.A.: The Selberg trace formula for PSL (2,R), vol. I. (Lect. Notes Math., vol. 548) Berlin Heidelberg New York: Springer 1976
[H3] Hejhal, D.A.: The Selberg trace formula for PSL (2,R), vol. II. (Lect. Notes Math., vol. 1001) Berlin Heidelberg New York: Springer 1983
[Hu] Huber, H.: Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. Math. Ann.138, 1–26 (1959)
[Hx] Huxley, M.N.: Scattering matrices for congruence subgroups. In: Rankin, R. (ed.) Modular forms, pp. 141–156. Chichester: Ellis Horwood 1984
[J] Jorgensen, T.: Simple geodesics on Riemann surfaces. Proc. Am. Math. Soc.86, 120–122 (1982)
[K] Kato, T.: Perturbation theory for linear operators. Berlin Heidelberg New York: Springer 1966
[Ke] Keen, L.: Canonical polygons for finitely generated Fuchsian groups. Acta Math.115, 1–16 (1966)
[Kr] Kra, I.: Automorphic Forms and Kleinian Groups. Reading, Mass.: Benjamin 1972
[LP] Lax, P., Phillips, R.: Scattering theory for automorphic forms.l (Ann. Math. Stud., vol. 87) Princeton: Princeton University Press 1976
[L] Lundelius, R.: Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume. Ph.D. Thesis, Stanford University, Stanford (1990)
[Mc] McKean, H.P.: Selberg's trace formula as applied to a compact Riemann surface. Commun. Pure Appl. Math.25, 225–246 (1972)
[MO] Magnus, W., Oberhettinger, F., Soni, R.: Special functions of mathematical physics. Berlin Heidelberg New York: Springer 1966
[Mü1] Müller, W.: Spectral theory for Riemannian manifolds with cusps and a related trace formula. Math. Nachr.111, 197–288 (1983)
[Mü2] Müller, W.: The point spectrum and spectral geometry for Riemannian manifolds with cusps. Math. Nachr.125, 243–257 (1986)
[Mf] Mumford, D.: A remark on Mahler's compactness theorem. Proc. Am. Math. Soc.28, 289–294 (1971)
[OPS1] Osgood, B., Phillips, R., Sarnak, P.: Extremals of determinants of Laplacians. J. Funct. Anal.80, 148–211 (1988)
[OPS2] Osgood, B., Phillips, R., Sarnak, P.: Compact isospectral sets of surfaces. J. Funct. Anal.80, 212–234 (1988)
[PS1] Phillips, R., Sarnak, P.: Perturbation theory for the Laplacian on automorphic functions. Am. Math. Soc.5, 1–32 (1992)
[PS2] Phillips, R., Sarnak, P.: On cusp forms for cofinite subgroups of PSL (2,R). Invent. Math.80, 339–364 (1985)
[P] Prachar, K.: Primzahlverteilung. Berlin Heidelberg New York: Springer 1957
[Se1] Selberg, A.: Harmonic Analysis. In: Collected papers, vol. I., pp. 626–674. Berlin Heidelberg New York: Springer 1989
[Se2] Selberg, A.: Remarks on the distribution of poles of Eisenstein series. In: Gelbart, S., Howe, R., Sarnak, P. (eds.) Israel Math. Conf. Proc., vol. 3, part II. Festschrift in honor of I.I. Piatetski-Shapiro pp. 251–278. Jerusalem: Weizman 1990
[Su] Sunada, T.: Riemannian coverings and isospectral manifolds. Ann. Math.121, 169–186 (1985)
[T] Titchmarsh, E.C.: The theory of functions. London: Oxford University Press. 1950
[V] Vignéras, M.F.: Variétés riemanniennes isospectrales et non isométriques. Ann. Math.112, 21–32 (1980)
[W] Wolpert, S.: The length spectra as moduli for compact Riemann surfaces. Ann. Math.109, 323–351 (1979)
[Z] Zelditch, S.: Kuznecov sum formulae and Szegö limit formulae on manifolds. (Preprint, Johns Hopkins University 1991)
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Oblatum 27-III-1991 & 13-I-1992
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Müller, W. Spectral geometry and scattering theory for certain complete surfaces of finite volume. Invent Math 109, 265–305 (1992). https://doi.org/10.1007/BF01232028
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DOI: https://doi.org/10.1007/BF01232028