ArticleOriginal scientific text
Title
The asymptotic distribution of Kloosterman sums
Authors 1
Affiliations
- Mathematisches Institut, Bunsenstr. 3-5, D-37073 Göttingen, Germany
Bibliography
- R. W. Bruggeman and R. J. Miatello, Estimates of Kloosterman sums for groups of real rank one, Duke Math. J. 80 (1995), 105-137.
- J. W. Cogdell and I. I. Piatetski-Shapiro, The Arithmetic and Spectral Analysis of Poincaré Series, Perspect. Math. 13, Academic Press, 1990.
- H. Davenport, On certain exponential sums, J. Reine Angew. Math. 169 (1933), 158-176.
- W. Duke and H. Iwaniec, A relation between cubic exponential and Kloosterman sums, in: Contemp. Math. 143, Amer. Math. Soc., 1993, 255-258.
- T. Estermann, Vereinfachter Beweis eines Satzes von Kloosterman, Abh. Math. Sem. Hamburg 7 (1929), 82-98.
- T. Estermann, On Kloosterman's sum, Mathematika 2 (1961), 83-86.
- Y. Z. Flicker, Automorphic forms on covering groups of GL(2), Invent. Math. 57 (1980), 119-182.
- I. M. Gel'fand, M. I. Graev and I. I. Piatetski-Shapiro, Representation Theory and Automorphic Functions, W. B. Saunders, 1969.
- D. Goldfeld and P. Sarnak, Sums of Kloosterman sums, Invent. Math. 71 (1983), 243-250.
- C. Hooley, On the distribution of the roots of polynomial congruences, Mathematika 11 (1964), 39-49.
- N. Katz, Gauss Sums , Kloosterman Sums and Monodromy Groups, Ann. of Math. Study 116, Princeton Univ. Press, 1988.
- D. A. Kazhdan and S. J. Patterson, Metaplectic forms, Publ. Math. I.H.E.S. 59 (1984), 35-142.
- H. D. Kloosterman, Asymptotische Formeln für die Fourierkoeffizienten ganzer Modulformen, Abh. Math. Sem. Hamburg 5 (1927), 337-352.
- N. V. Kuznetsov, Peterson's hypothesis for parabolic forms of weight zero and Linnik's hypothesis. Sums of Kloosterman sums, Mat. Sb. 111 (1980), 334-383 (in Russian).
- S. Lang, Cyclotomic Fields, Grad. Texts in Math. 59, Springer, 1978.
- J. Lehner, Discontinuous Groups and Automorphic Functions, Amer. Math. Soc., 1964.
- A. V. Malyshev, Generalized Kloosterman sums and their applications, Vestnik Leningrad. Univ. 13 (1960), 59-75 (in Russian).
- I. Piatetski-Shapiro, Invariant theory and Kloosterman sums, in: Algebraic Groups, Proceedings of a Symposium in Utrecht, Lecture Notes in Math. 1271, Springer, 1987, 229-236.
- H. Salié, Zur Abschätzung der Fourierkoeffizienten ganzer Modulformen, Math. Z. 36 (1932), 263-278.
- P. Sarnak, Additive number theory and Maass forms, in: Lecture Notes in Math. 1052, Springer, 1984, 286-309.
- G. Stevens, Poincaré series on GL(r) and Kloosterman sums, Math. Ann. 277 (1987), 25-51.
- G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, 1944.
- A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-207 = Collected Papers, Vol. I, 1948, 386-389.
- D. J. Wright, Cubic character sums of cubic polynomials, Proc. Amer. Math. Soc. 100 (1987), 409-413.