The additive divisor problem and its analogs for Fourier coefficients of cusp forms. I

Mathematische Zeitschrift

Volumn 223, Issue 3, 1996, Pages 435-461

  Jutila, Matti ^a  

^a UNIVERSITY OF TURKU   (Finland)

Author keywords

[No Author keywords available]

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EID: 0030273960     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/pl00004270     Document Type: Article

References (30)

1. Duke, W, Iwaniec, H: Estimates for Coefficients of L-functions. In: Proc. Amalfi Conference on Analytic Number Theory, pp. 71-82, Università di Salerno 1992
2. Epstein, C., Hafner, J. L., Sarnak, P.: Zeros of L-functions Attached to Maass Forms. Math. Z. 190, 113-128 (1985)
3. Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Tables of Integral Transforms. New York Toronto London: Mc Graw-Hill 1953
4. Good, A.: Cusp Forms and Eigenfunctions of the Laplacian. Math. Ann. 255, 523-548 (1981)
5. Good, A.: On Various Means Involving the Fourier Coefficients of Cusp Forms. Math. Z. 183, 95-129 (1983)
6. Hafner, J. L.: Explicit Estimates in the Arithmetic Theory of Cusp Forms and Poincaré Series. Math. Ann. 264, 9-20 (1983)
7. Hafner, J. L.: On the zeros of Maass wave form L-functions. Bull. Amer. Math. Soc. 15, 61-64 (1986)
8. Ivić, A.: The Riemann zeta-function. New York: John Wiley& Sons 1985
9. Ivić, A., Motohashi, Y.: The mean square of the error term for the fourth power mean of the zeta-function. Proc. London Math. Soc. (3) 69, 309-329 (1994)
10. Iwaniec, H.: Fourier coefficients of cusp forms and the Riemann zeta-function. In: Séminaire de Théorie des Nombres Bordeaux 1979/1980, exposé no 18
11. Iwaniec, H.: Mean values for Fourier coefficients of cusp forms and sums of Kloosterman sums. In: Journées Arithmétiques de Exeter 1980, pp. 306-321, Cambridge: Cambridge University Press 1982
12. Iwaniec, H.: The spectral growth of automorphic L-functions. J. reine angew. Math. 428, 139-159 (1992)
13. Jutila, M.: Lectures on a Method in the Theory of Exponential Sums. Tata Institute of Fundamental Research, Bombay (Lectures on Mathematics and Physics, vol. 80), Berlin Heidelberg New York Tokyo: Springer 1987.
14. Jutila, M.: The Additive Divisor Problem and Exponential Sums. In: Advances in Number Theory, pp. 113-135, Oxford: Clarendon Press 1993
15. Jutila, M.: On Spectral Large Sieve Inequalities (to appear)
16. Jutila, M., Motohashi, Y.: Mean value estimates for exponential sums and L-functions: a spectral theoretic approach. J. reine angew. Math. 459, 61-87 (1995)
17. Kuznetsov, N. V: Petersson's conjecture for cusp forms of weight zero and Linnik's conjecture. Sums of Kloosterman sums (in Russian). Mat. Sb. 111, 334-383 (1980)
18. Kuznetsov, N. V.: On the mean value of the Hecke series of a cusp form of weight zero (in Russian). Zap. Nauch. Sem. LOMI 109, 93-130 (1981)
19. Kuznetsov, N. V.: Convolution of the Fourier coefficients of the Eisenstein-Maass series (in Russian). Zap. Nauch. Sem. LOMI 129, 43-84 (1983)
20. Lebedev, N. N.: Special functions and their applications. New York: Dover Publications Inc. 1972
21. Luo, W.: Spectral Mean-values of Automorphic L-functions at Special Points (to appear)
22. Meurman, T.: On exponential sums involving the Fourier coefficients of Maass wave forms. J. Reine Angew. Math. 384, 192-207 (1988)
23. Montgomery, H. L.: Topics in multiplicative number theory. (Lecture Notes in Mathematics, vol. 227) Berlin Heidelberg New York: Springer 1971
24. m(r), π). Canadian Math. Bull. 28, 408-410 (1985)
25. Motohashi, Y.: The Binary Additive Divisor Problem. Ann. Sci. l'Ecole Norm. Sup. 27, 529-572 (1994)
26. Sarnak, P.: Integrals of products of eigenfunctions. Int. Math. Res. Not. 6, 251-260 (1994)
27. Tichmarsh, E. C.: The Theory of the Riemann Zeta-function, 2nd edn. Oxford: Clarendon Press 1986
28. Tahtadjan, L. A., Vinogradov, A. I.: The zeta-function of the additive divisor problem and the spectral decomposition of the automorphic Laplacian (in Russian). Zap. Nauch. Sem. LOMI 134, 84-116 (1984)
29. Whittaker, E. T., Watson, G. N.: A Course of Modern Analysis. Cambridge: Cambridge Univ. Press 1950
30. Zagier, D.: The Rankin-Selberg method for automorphic functions which are not of rapid decay. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28, 415-437 (1981)