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Sums of Kloosterman sums. (English) Zbl 0507.10029


MSC:

11L40 Estimates on character sums

Citations:

Zbl 0451.10022
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References:

[1] Bruggeman, R.W.: Fourier coefficients of cusp forms. Invent. Math.45, 1-18 (1978) · Zbl 0363.10018
[2] Davenport, H.: On certain exponential sums. J. für Mathematik169, 158 (1933) · JFM 59.0370.03
[3] Davenport, H.: Multiplicative number theory. Berlin-Heidelberg-New York: Springer 1980 · Zbl 0453.10002
[4] Deshouillers, J.M., Iwaniec, H.: Kloosterman sums and Fourier coefficients of cusp forms. Preprint 1981 · Zbl 0502.10021
[5] Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series, and products. New York: Academic Press 1980 · Zbl 0521.33001
[6] Hardy, G., Riesz, M.: Dirichlet series. Cambridge: Cambridge University Press 1915 · JFM 45.0387.03
[7] Kuznetsov, N.V.: Peterson hypothesis, for parabolic forms of weight zero and Linnik hypothesis. Sums of Kloosterman sums. Math. Sbornik111, (153, no. 3) 334-383 (1980) · Zbl 0427.10016
[8] Linnik, Y.V.: Additive problems and eigenvalues of the modular operators. Proc. Internat. Congr. Math. Stockholm 1962, pp. 270-284
[9] Proskurin, N.V.: Summation formulas for generalized Kloosterman sums. Zap. Navcn. Sem. Leningrad Otdel. Mat. Inst. Steklov82, 103-135 (1979) · Zbl 0425.10027
[10] Riesz, F., Nagy, B.: Functional analysis. New York: Frederick Ungar Publishing Company 1978 · Zbl 0070.10902
[11] Roelcke, W.: Das Eigenwertproblem der automorphen Formen... Math. Ann.167, 292-337 (1966) · Zbl 0152.07705
[12] 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. · Zbl 0142.33903
[13] Vardi, I.: Mass. Inst. Tech. Ph.D. Thesis, 1982
[14] Weil, A.: On some exponential sums. Proc. Natl. Acad. Sci. USA34, 204-207 (1948) · Zbl 0032.26102
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