A relation between the Riemann zeta-function and the hyperbolic laplacian

 Access to full text

 Full (PDF)

1. [1] R.J. Anderson - H.M. Stark, Oscillation theorems, Lecture Notes in Math.899, Springer Verlag, Berlin, 1981, 79-106. Zbl0472.10044MR654520
2. [2] F.V. Atkinson, The mean value of the Riemann zeta-function, Acta Math.81 (1949), 353-376. Zbl0036.18603MR31963
3. [3] A. Ivić, Mean Values of the Riemann Zeta-Function, Lect. Math. Phys.82, Tata Institute, Bombay, 1991. Zbl0758.11036
4. [4] A. Ivić - Y. Motohashi, The mean square of the error term in the fourth moment of the zeta-function, Proc. London Math. Soc.69 (1994), 309-329. Zbl0805.11060MR1281967
5. [5] A. Ivić - Y. Motohashi, On the fourth power moment of the Riemann zeta-function, J. Number Theory51 (1995), 16-45. Zbl0824.11048MR1321722
6. [6] M. Jutila, The additive divisor problem and exponential sums, Advances in Number Theory, Clarendon Press, Oxford, 1993, 113-135. Zbl0792.11037MR1368414
7. [7] Y. Motohashi, Spectral mean values of Maass waveform L-functions, J. Number Theory42 (1992), 258-284. Zbl0759.11026MR1189505
8. [8] Y. Motohashi, An explicit formula for the fourth power mean of the Riemann zeta-function, Acta Math.170 (1993), 181-220. Zbl0784.11042MR1226527
9. [9] Y. Motohashi, The fourth power mean of the Riemann zeta-function, Proc. Amalfi Intern. Symp. Analytic Number Theory, ed. E. Bombieri et al., Salerno, 1993, 325-344. Zbl0788.11034MR1220474
10. [10] Y. Motohashi, The binary additive divisor problem, Ann. Sci. École Norm. Sup.27 (1994), 529-572. Zbl0819.11038MR1296556
11. [11] Y. Motohashi, A note on the mean value of the zeta and L-functions. VIII, Proc. Japan Acad. Ser. A70 (1994), 190-193. Zbl0812.11050MR1291180
12. [12] Y. Motohashi, The Riemann zeta-function and the non-Euclidean Laplacian, AMS Sugaku Exposition, to appear. Zbl0844.11056MR1256466
13. [13] L.A. Takhtadjan - A.I. Vinogradov, The zeta-function of the additive divisor problem and the spectral decomposition of the automorphic Laplacian, Sem. LOMI, AN SSSR134 (1984), 84-116 (Russian). Zbl0536.10025MR741855
14. [14] B. Szyd, A note on oscillations in the additive divisor problem, I, Preprint, 1993. 

1. Aleksandar Ivić, Matti Jutila, Yoichi Motohashi, The Mellin transform of powers of the zeta-function
2. Jerzy Kaczorowski, Bogdan Szydło, Some $\Omega$-results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem