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1994 | 68 | 4 | 341-368
Tytuł artykułu

Sums of coefficients of Hecke series

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
68
Numer
4
Strony
341-368
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-12-02
Twórcy
  • Katedra Matematike RGF-A, Universiteta u Beogradu, Djušina 7, 11000 Beograd, (Serbia) Yugoslavia
autor
  • Department of Mathematics, University of Turku, Sf-20500 Turku, Finland
Bibliografia
  • [1] D. Bump, The Rankin-Selberg method: a survey, in: Number Theory, Trace Formulas and Discrete Groups, Sympos. in honor of A. Selberg (Oslo, 1987), Academic Press, Boston, 1989, 49-109.
  • [2] D. Bump, W. Duke, D. Ginsburg, J. Hoffstein and H. Iwaniec, An estimate for Fourier coefficients of Maass wave forms, Duke Math. J. 66 (1992), 75-81.
  • [3] K. Chandrasekharan and R. Narasimhan, Functional equations with multiple gamma-factors and the average order of arithmetical functions, Ann. of Math. 76 (1962), 93-136.
  • [4] K. Chandrasekharan and R. Narasimhan, On the mean value of the error term for a class of arithmetical functions, Acta Math. 112 (1964), 41-67.
  • [5] J.-M. Deshouillers and H. Iwaniec, The non-vanishing of the Rankin-Selberg zeta-functions at special points, in: Selberg Trace Formulas, Contemp. Math. 53, Amer. Math. Soc., Providence, R.I., 1986, 51-95.
  • [6] A. Erdélyi et al ., Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953.
  • [7] J. L. Hafner and A. Ivić, On sums of Fourier coefficients of cusp forms, Enseign. Math. 35 (1989), 375-382.
  • [8] A. Ivić, The Riemann Zeta-Function, Wiley, New York, 1985.
  • [9] A. Ivić, Lectures on Mean Values of the Riemann Zeta-Function, Tata Inst. Fund. Res. Lect. Notes 82, Bombay, 1991, Springer, Berlin, 1991.
  • [10] A. Ivić and Y. Motohashi, A note on the mean value of the zeta and L-functions. VII, Proc. Japan Acad. Ser. A 66 (1990), 150-152.
  • [11] H. Iwaniec, Fourier coefficients of cusp forms and the Riemann zeta-function, Séminaire de Théorie des Nombres, Université Bordeaux 1979/80, exp. no. 18.
  • [12] H. Iwaniec, Non-holomorphic modular forms and their applications, in: Modular Forms, R. A. Rankin (ed.), Sympos. Durham 1983, Halsted Press, New York, 1984, 157-196.
  • [13] H. Iwaniec, Promenade along modular forms and analytic number theory, in: Topics in Analytic Number Theory, S. W. Graham and J. D. Vaaler (eds.), University of Texas Press, Austin, Texas, 1985, 221-303.
  • [14] H. Iwaniec, Small eigenvalues of the Laplacian for Γ₀(N), Acta Arith. 56 (1990), 65-82.
  • [15] H. Iwaniec, The spectral growth of automorphic L-functions, J. Reine Angew. Math. 428 (1992), 139-159.
  • [16] M. Jutila, A Method in the Theory of Exponential Sums, Tata Inst. Fund. Res. Lect. Notes 80, Bombay, 1987, Springer, Berlin, 1987.
  • [17] N. V. Kuznetsov, Petersson hypothesis for forms of weight zero and Linnik's conjecture. Sums of Kloosterman sums, Math. USSR-Sb. 39 (1981), 299-342.
  • [18] N. V. Kuznetsov, Mean value of Hecke series associated with cusp forms of weight zero, Zap. Nauchn. Sem. LOMI 109 (1981), 93-130 (in Russian).
  • [19] N. V. Kuznetsov, Convolution of the Fourier coefficients of the Eisenstein-Maass series, Zap. Nauchn. Sem. LOMI 129 (1983), 43-84 (in Russian).
  • [20] T. Meurman, On exponential sums involving the Fourier coefficients of Maass wave forms, J. Reine Angew. Math. 384 (1985), 192-207.
  • [21] T. Meurman, On the mean square of the Riemann zeta-function, Quart. J. Math. (Oxford) (2) 38 (1987), 337-343.
  • [22] C. Moreno and F. Shahidi, The L-functions $L(s,Sym^m(r),π)$, Canad. Math. Bull. 28 (1985), 405-410.
  • [23] Y. Motohashi, A note on the mean value of the zeta and L-functions. VI, Proc. Japan Acad. Ser. A 65 (1989), 273-275.
  • [24] Y. Motohashi, An explicit formula for the fourth power mean of the Riemann zeta-function, Acta Math. 170 (1993), 181-220.
  • [25] M. R. Murty, On the estimation of eigenvalues of Hecke operators, Rocky Mountain J. Math. 15 (1985), 521-533.
  • [26] E. Preissmann, Sur la moyenne quadratique du terme de reste du problème du cercle, C. R. Acad. Sci. Paris Sér. I 306 (1988), 151-154.
  • [27] N. V. Proskurin, Convolution of Dirichlet series with Fourier coefficients of parabolic forms of weight zero, Zap. Nauchn. Sem. LOMI 93 (1980), 204-217 (in Russian).
  • [28] R. A. Rankin, Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions II. The order of the Fourier coefficients of integral modular forms, Proc. Cambridge Philos. Soc. Math. 35 (1939), 357-372.
  • [29] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., Clarendon Press, Oxford, 1986.
  • [30] K.-C. Tong, On divisors problems III, Acta Math. Sinica 6 (1956), 515-541 (in Chinese).
  • [31] G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, Cambridge, 1944.
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Bibliografia
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