The binary additive divisor problem
Motohashi, Yoichi
Annales scientifiques de l'École Normale Supérieure, Tome 27 (1994), p. 529-572 / Harvested from Numdam
@article{ASENS_1994_4_27_5_529_0,
     author = {Motohashi, Yoichi},
     title = {The binary additive divisor problem},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {27},
     year = {1994},
     pages = {529-572},
     doi = {10.24033/asens.1700},
     mrnumber = {95i:11104},
     zbl = {0819.11038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1994_4_27_5_529_0}
}
Motohashi, Yoichi. The binary additive divisor problem. Annales scientifiques de l'École Normale Supérieure, Tome 27 (1994) pp. 529-572. doi : 10.24033/asens.1700. http://gdmltest.u-ga.fr/item/ASENS_1994_4_27_5_529_0/

[1] F.V. Atkinson, The Mean Value of the Zeta-function on the Critical Line (Proc. London Math. Soc., Vol. 47, 1941, pp. 174-200). | JFM 67.0985.02 | MR 3,70a | Zbl 0028.39002

[2] F.V. Atkinson, The Mean Value of the Riemann Zeta-function (Acta Math., Vol. 81, 1949, pp. 353-376). | MR 11,234d | Zbl 0036.18603

[3] P. Deligne, La Conjecture de Weil (Publ. Math. I.H.E.S., Vol. 43, 1974, pp. 273-307). | Numdam | MR 49 #5013 | Zbl 0287.14001

[4] J.-M. Deshouillers, Sur quelques moyennes des coefficients de Fourier de formes modulaires (Lect. Notes in Math., Springer, Vol. 1068, 1984, pp. 74-79). | MR 756084 | Zbl 0539.10022

[5] J.-M. Deshouillers and H. Iwaniec, An Additive Divisor Problem (J. London. Math. Soc., Vol. 26(2), 1982, pp. 1-14). | MR 84b:10067 | Zbl 0462.10030

[6] J.-M. Deshouillers and H. Iwaniec, Kloosterman Sums and Fourier Coefficients of Cusp Forms (Invent. math. Vol. 70, 1982, pp. 219-288). | MR 84m:10015 | Zbl 0502.10021

[7] T. Estermann, On the Representation of a Number as the Sum of Two Products (Proc. London. Math. Soc., Vol. 31, 1930, pp. 123-133). | JFM 56.0174.02

[8] T. Estermann, Über die Darstellung einer Zahl als Differenz von zwei Produkten (J. Reine Angew. Math., Vol. 164, 1931, pp. 173-182). | JFM 57.0222.01 | Zbl 0001.20302

[9] H. Halberstam, An Asymptotic Formula in the Theory of Numbers (Trans. A.M.S., Vol. 84, 1957, pp. 338-351). | MR 18,874b | Zbl 0087.04304

[10] D.R. Heath-Brown, The Fourth Power Moment of the Riemann Zeta-function (Proc. London Math. Soc., Vol. 38(3), 1979, pp. 385-422). | MR 81f:10052 | Zbl 0403.10018

[11] A.E. Ingham, Some Asymptotic Formulae in the Theory of Numbers (J. London Math. Soc., Vol. 2, 1927, pp. 202-208). | JFM 53.0157.01

[12] A. Ivić, Mean Values of the Riemann Zeta-function (Tata Lect. Notes in Math., Vol. 82, 1992).

[13] A. Ivić and Y. Motohashi, A Note on the Mean Value of the Zeta and L-functions (VII. Proc. Japan Acad., Vol. 66A, 1990, pp. 150-152). | MR 91h:11086 | Zbl 0699.10056

[14] A. Ivić and Y. Motohashi, On the Fourth Power Moment of the Riemann Zeta-function, to appear in J. Number Theory. | Zbl 0824.11048

[15] A. Ivić and Y. Motohashi, The Mean Square of the Error Term for the Fourth Moment of the Zeta-function, to appear in Proc. London Math. Soc. | Zbl 0805.11060

[16] H. Iwaniec, Fourier Coefficients of Cusp Forms and The Riemann Zeta-function (Exp. n° 18, Sem. Th. Nombres, Univ. Bordeaux, 1979/1980). | Zbl 0438.10030

[17] M. Jutila, A Method in the Theory of Exponential Sums (Tata Lect. Notes in Math., Vol. 80, 1987). | MR 89g:11069

[18] M. Jutila, The Additive Divisor Problem and Exponential Sums (Advances in Number Theory, Clarendon Press, Oxford, 1993, pp. 113-135). | MR 96m:11084 | Zbl 0792.11037

[19] N.V. Kuznetsov, Petersson Hypothesis for Forms of Weight Zero and Linnik Hypothesis, Preprint, 1977 (Russian).

[20] N.V. Kuznetsov, Spectral Method for Arithmetical Problems (Zap. Nauch. Sem., LOMI 76, 1978, pp. 159-166). | MR 81b:10019 | Zbl 0419.10043

[21] N.V. Kuznetsov, Petersson Hypothesis for Parabolic Forms of Weight Zero and Linnik Hypothesis. Sums of Kloosterman sums (Math. Sbornik, Vol. 111, 1980, pp. 334-383). | MR 81m:10053 | Zbl 0427.10016

[22] N.V. Kuznetsov, Convolution of the Fourier Coefficients of the Eisenstein-Maass Series (Zap. Nauch. Sem., LOMI 129, 1983, pp. 43-84). | MR 86h:11039 | Zbl 0496.10013

[23] C. Moreno et F. Shahidi, The L-functions L(s, Symm(r), π) (Canadian Math. Bull., Vol. 28, 1985, pp. 405-410). | MR 87a:11051 | Zbl 0577.10027

[24] Y. Motohashi, A Note on the Mean Value of the Zeta and L-functions. VI (Proc. Japan Acad., Vol. 65A, 1989, pp. 273-275). | MR 91c:11049 | Zbl 0699.10055

[25] Y. Motohashi, An Explicit Formula for the Fourth Power Mean of the Riemann Zeta-function (Acta Mathematica, Vol. 170, 1993, pp. 181-220). | MR 94d:11065 | Zbl 0784.11042

[26] Y. Motohashi, Spectral Mean Values of Maass Wave Form L-functions (J. Number Theory, Vol. 42, 1992, pp. 258-284). | MR 93m:11041 | Zbl 0759.11026

[27] Y. Motohashi, Kuznetsov's trace formulas, Manuscript, 1991.

[28] R. Murty, On the Estimation of Eigen Values of Hecke Operators (Rocky Mountain J. Math., Vol. 15, 1985, pp. 521-533). | Zbl 0588.10027

[29] A. Selberg, On the Estimation of Fourier Coefficients of Modular Forms (Proc. Symp. Pure Math., Vol. 8, 1965, pp. 1-15). | MR 32 #93 | Zbl 0142.33903

[30] L. A. Tahtadjan and A. I. Vinogradov, The Zeta-function of the Additive Divisor Problem and the Spectral Decomposition of the Automorphic Laplacian (Zap. Nauch. Sem., LOMI 134, 1984, pp. 84-116, Russian). | Zbl 0536.10025

[31] N. I. Zavorotnyi, On the Fourth Moment of the Riemann Zeta-function, Preprint, 1986 (Russian).