@article{bwmeta1.element.bwnjournal-article-aav68i4p341bwm,
author = {Aleksandar Ivi\'c and Tom Meurman},
title = {Sums of coefficients of Hecke series},
journal = {Acta Arithmetica},
volume = {68},
year = {1994},
pages = {341-368},
zbl = {0812.11054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav68i4p341bwm}
}
Aleksandar Ivić; Tom Meurman. Sums of coefficients of Hecke series. Acta Arithmetica, Tome 68 (1994) pp. 341-368. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav68i4p341bwm/
[000] [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.
[001] [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. | Zbl 0760.11017
[002] [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. | Zbl 0211.37901
[003] [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. | Zbl 0128.26302
[004] [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.
[005] [6] A. Erdélyi et al ., Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953. | Zbl 0051.30303
[006] [7] J. L. Hafner and A. Ivić, On sums of Fourier coefficients of cusp forms, Enseign. Math. 35 (1989), 375-382. | Zbl 0696.10020
[007] [8] A. Ivić, The Riemann Zeta-Function, Wiley, New York, 1985.
[008] [9] A. Ivić, Lectures on Mean Values of the Riemann Zeta-Function, Tata Inst. Fund. Res. Lect. Notes 82, Bombay, 1991, Springer, Berlin, 1991. | Zbl 0758.11036
[009] [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.
[010] [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. | Zbl 0438.10030
[011] [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.
[012] [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. | Zbl 0599.10017
[013] [14] H. Iwaniec, Small eigenvalues of the Laplacian for Γ₀(N), Acta Arith. 56 (1990), 65-82. | Zbl 0702.11034
[014] [15] H. Iwaniec, The spectral growth of automorphic L-functions, J. Reine Angew. Math. 428 (1992), 139-159. | Zbl 0746.11024
[015] [16] M. Jutila, A Method in the Theory of Exponential Sums, Tata Inst. Fund. Res. Lect. Notes 80, Bombay, 1987, Springer, Berlin, 1987.
[016] [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. | Zbl 0461.10017
[017] [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). | Zbl 0446.10023
[018] [19] N. V. Kuznetsov, Convolution of the Fourier coefficients of the Eisenstein-Maass series, Zap. Nauchn. Sem. LOMI 129 (1983), 43-84 (in Russian). | Zbl 0496.10013
[019] [20] T. Meurman, On exponential sums involving the Fourier coefficients of Maass wave forms, J. Reine Angew. Math. 384 (1985), 192-207. | Zbl 0627.10017
[020] [21] T. Meurman, On the mean square of the Riemann zeta-function, Quart. J. Math. (Oxford) (2) 38 (1987), 337-343. | Zbl 0624.10032
[021] [22] C. Moreno and F. Shahidi, The L-functions , Canad. Math. Bull. 28 (1985), 405-410. | Zbl 0577.10027
[022] [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. | Zbl 0699.10055
[023] [24] Y. Motohashi, An explicit formula for the fourth power mean of the Riemann zeta-function, Acta Math. 170 (1993), 181-220. | Zbl 0784.11042
[024] [25] M. R. Murty, On the estimation of eigenvalues of Hecke operators, Rocky Mountain J. Math. 15 (1985), 521-533. | Zbl 0588.10027
[025] [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. | Zbl 0654.10042
[026] [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).
[027] [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. | Zbl 0021.39202
[028] [29] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., Clarendon Press, Oxford, 1986. | Zbl 0601.10026
[029] [30] K.-C. Tong, On divisors problems III, Acta Math. Sinica 6 (1956), 515-541 (in Chinese).
[030] [31] G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, Cambridge, 1944. | Zbl 0063.08184