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References
[Bru] Bruggeman, R.W.: Fourier coefficients of cusp forms. Invent. Math.45, 1–18 (1978)
[Bus] Buser, P.: On Cheeger's inequalityλ 1≧h 2/4. Proc. Symposia, in Pure Math., XXXVI, pp. 29–77 AMS, Providence 1981
[Che] Cheeger, J.: A lower bound for the smallest eigenvalue of the Laplacian. Problems in Analysis, A symposium in honour of Bochner, Princeton University Press, Princeton, N.J. 1970 pp. 195–199
[Del] Deligne, P.: La conjecture de Weil I. Publ. Math. I.H.E.S.,43, 273–307 (1974)
[Dl 1] Deshouillers, J.-M., Iwaniec, H.: On the greatest prime factor ofn 2+1 Ann. Inst. Fourier. in press (1982)
[DI2] Deshouillers, J.-M., Iwaniec, H.: An additive divisor problem. J. London Math. Soc.26, (2), 1–14 (1982)
[Di3] Deshouillers, J.-M., Iwaniec, H.: Power mean-values for the Riemann zeta-function. Mathematika in press (1982)
[DI4] Deshouillers, J.-M., Iwaniec, H.: On the Brun-Titchmarsh theorem and the greatest prime factor ofp+a. Proc. Janos Bolyai Soc. Conf. in press (1982)
[EMOT] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions II. New York-Toronto-London: Mc Graw-Hill 1953
[Fad] Faddeev, L.D.: Expansions in eigenfunctions of the Laplace operator in the fundamental domain of a discrete group on the Lobačevskii plane. Trudy Moscov, Mat. Obsc.,17, 323–350 (1967)
[G-R] Gradsztejn, I.S., Ryżyk, I.M.: Tablice całek, sum, szeregów i iloczynow. PWN-Warszawa, 1964
[Gun] Gunning, R.C.: Lectures on modular forms. Princeton University Press, 1962
[H.-B.] Heath-Brown, D.R.: The fourth power moment of the Riemann zeta-function. Proceeding London Math. Soc.38(3), 385–422 (1979)
[Hej] Hejhal, D.A.: Some observations concerning eigenvalues of the Laplacian and DirichletL-series in Recent progress in analytic number theory. London: Academic Press 1981
[Hoo] Hooley, C.: On the greatest prime factor of a quadratic polynomial. Acta Math.117, 281–299 (1967)
[Iwa 1] Iwaniec, H.: Fourier coefficients of cusp forms and the Riemann zeta-function. Sém. Th. Nb. Bordeaux (1979–1980), exposé no18,36 pages
[Iwa 2] Iwaniec, H.: Mean values for Fourier coefficients of cusp forms and sums of Kloosterman sums. Proceedings from the Journées Arithmétiques at Exeter in press (1982)
[Iwa 3] Iwaniec, H.: On mean values for Dirichlet's polynomials and the Riemann zeta-function. J. London Math. Soc.22, (2), 39–45 (1980)
[Iwa 4] Iwaniec, H.: On the Brun-Titchmarsh theorem. J. Math. Soc. Japan34, 95–123 (1982)
[Kub] Kubota, T.: Elementary Theory of Eisenstein Series. New-York: John Wiley and Sons 1973
[Kuz1] Kuznietsov, N.V.: Petersson hypothesis for forms of weight zero and Linnik hypothesis (in Russian), Preprint no02, Khab. KHII, Khabarovsk 1977
[Kuz2] Kuznietsov, N.V.: Petersson hypothesis for parabolic forms of weight zero and Linnik hypothesis. Sums of Kloostermann sums. Math. Sbornik111, (153), no3, 334–383 (1980)
[Lin] Linnik, Yu.V.: Additive problems and eigenvalues of the modular operators. Proc. Internat. Congr. Math. Stockholm 270–284 (1962)
[Maa1] Maass, H.: Über eine neue Art von nichtanalytischen automorphen Funktionen. Math. Ann.121, (o2) 141–183 (1949)
[Maa2] Maass, H.: On modular functions of one complex variable. Tata Institute, Bombay, 1964
[Mon] Montgomery, H.L.: Topics in multiplicative number theory. Lect. Notes in Math. vol. 227. Berlin-New-York: Springer 1971
[Pet] Petersson, H.: Über die Entwicklungskoeffizienten der automorphen Formen. Acta Math.58, 169–215 (1932)
[Pro1] Proskurin, N.V.: Summation formulas for generalized Kloosterman sums (in Russian). Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.82, 103–135 (1979)
[Pro2] Proskurin, N.V.: On a hypothesis of Yu.V. Linnik (in Russian). Zap. Naučn. Sem. Leningrad Otdel. Mat. Inst. Steklov.91, 94–118 (1979)
[Pro3] Proskurin, N.V.: The estimations of the eigenvalues of Hecke's operators in the space of parabolic forms of weight zero. Studies in Number Theory, vol. 5, 136–143 (1979). Pub. Math. Inst. Steklov
[Ran] Rankin, R.: Modular forms and functions. Cambridge-London-New-York: Cambridge University Press 1977
[Roe1] Roelcke, W.: Über die Wellengleichung bei Grenzkreisgruppen erster Art. Sitz. Ber. Heidl. Akad. der Wiss. (Math. natur. Kl.) 1956, 4. Abh.
[Roe2] Roelcke, W.: Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I. II. Math. Ann.167, 292–337 (1966);168, 261–324 (1967)
[Sel1] Selberg, A.: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet's series. J. Indian Mat. Soc.20, 47–87 (1956)
[Sel2] Selberg, A.: On the estimation of Fourier coefficients of modular forms. Proc. Symposia in Pure Math. VIII, A.M.S., Providence 1965, pp. 1–15
[Shi] Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Princeton: Princeton University Press 1971
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Deshouillers, J.M., Iwaniec, H. Kloosterman sums and Fourier coefficients of cusp forms. Invent Math 70, 219–288 (1982). https://doi.org/10.1007/BF01390728
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DOI: https://doi.org/10.1007/BF01390728