ArticleOriginal scientific text
Title
On oscillations in the additive divisor problem, 1
Authors 1
Affiliations
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
Bibliography
- R. J. Anderson and H. M. Stark, Oscillation theorems, in: Lecture Notes in Math. 899, Springer, 1981, 79-106.
- J.-M. Deshouillers and H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70 (1982), 219-288.
- J.-M. Deshouillers and H. Iwaniec, Additive divisor problem, J. London Math. Soc. (2) 26 (1982), 1-14.
- A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, II, McGraw-Hill, 1953.
- M. Jutila, The additive divisor problem and exponential sums, in: Third Conference of the Canadian Number Theory Association, Kingston 1991, Clarendon Press, Oxford, 1993, 113-135.
- T. Kubota, Elementary Theory of Eisenstein Series, Wiley, New York, 1973.
- N. V. Kuznetsov, Petersson's conjecture for cusp forms of weight zero and Linnik's conjecture. Sums of Kloosterman sums, Math. USSR-Sb. 39 (1981), 299-342.
- N. V. Kuznetsov, Convolutions of the Fourier coefficients of the Eisenstein-Maass series, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1983), 43-84 (in Russian).
- E. Landau, Über einen Satz von Tschebyschef, Math. Ann. 61 (1905), 527-550.
- Y. Motohashi, The binary additive divisor problem, Ann. Sci. École Norm. Sup., to appear.
- Y. Motohashi, Spectral mean values of Maass waveform L-functions, J. Number Theory 42 (1992), 258-284.
- N. V. Proskurin, Summation formulas for generalized Kloosterman sums, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 82 (1979), 103-135 (in Russian).
- L. A. Takhtajan and A. I. Vinogradov, The Gauss-Hasse hypothesis on real quadratic fields with class number one, J. Reine Angew. Math. 335 (1982), 40-87.
- L. A. Takhtajan and A. I. Vinogradov, The zeta-function of the additive divisor problem and the spectral decomposition of the automorphic Laplacian, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1984), 84-116 (in Russian).
- E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed. revised by D. R. Heath-Brown, Clarendon Press, Oxford, 1986.