The binary additive divisor problem
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 27 (1994) no. 5, pp. 529-572.
@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},
     pages = {529--572},
     publisher = {Elsevier},
     volume = {Ser. 4, 27},
     number = {5},
     year = {1994},
     doi = {10.24033/asens.1700},
     zbl = {0819.11038},
     mrnumber = {95i:11104},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1700/}
}
TY  - JOUR
AU  - Motohashi, Yoichi
TI  - The binary additive divisor problem
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1994
DA  - 1994///
SP  - 529
EP  - 572
VL  - Ser. 4, 27
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.24033/asens.1700/
UR  - https://zbmath.org/?q=an%3A0819.11038
UR  - https://www.ams.org/mathscinet-getitem?mr=95i:11104
UR  - https://doi.org/10.24033/asens.1700
DO  - 10.24033/asens.1700
LA  - en
ID  - ASENS_1994_4_27_5_529_0
ER  - 
%0 Journal Article
%A Motohashi, Yoichi
%T The binary additive divisor problem
%J Annales scientifiques de l'École Normale Supérieure
%D 1994
%P 529-572
%V Ser. 4, 27
%N 5
%I Elsevier
%U https://doi.org/10.24033/asens.1700
%R 10.24033/asens.1700
%G en
%F ASENS_1994_4_27_5_529_0
Motohashi, Yoichi. The binary additive divisor problem. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 27 (1994) no. 5, pp. 529-572. doi : 10.24033/asens.1700. http://www.numdam.org/articles/10.24033/asens.1700/

[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 | MR | Zbl

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

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

[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 | Zbl

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

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

[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

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

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

[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 | Zbl

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

[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 | Zbl

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

[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

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

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

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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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

[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

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

[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

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

Cited by Sources: