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2000 | 95 | 4 | 305-342
Tytuł artykułu

The Mellin transform of powers of the zeta-function

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
95
Numer
4
Strony
305-342
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-09-29
poprawiono
2000-01-31
Twórcy
  • Katedra Matematike RGF-a, Universiteta u Beogradu, Djušina 7, 11000 Beograd, Serbia (Yugoslavia)
autor
  • Department of Mathematics, University of Turku, FIN-20014 Turku, Finland
  • Department of Mathematics, College of Science and Technology, Nihon University, Surugadai, Tokyo-101, Japan
Bibliografia
  • [1] F. V. Atkinson, The mean value of the Riemann zeta-function, Acta Math. 81 (1949), 353-376.
  • [2] H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953.
  • [3] J. L. Hafner and A. Ivić, On the mean square of the Riemann zeta-function on the critical line, J. Number Theory 32 (1989), 151-191.
  • [4] A. Ivić, The Riemann Zeta-Function, Wiley, New York, 1985.
  • [5] A. Ivić, Mean Values of the Riemann Zeta-Function, Tata Inst. Fund. Res. Lectures 82, Bombay, 1991 (distr. by Springer, Berlin).
  • [6] A. Ivić, The Mellin transform and the Riemann zeta-function, in: Proc. Conference on Elementary and Analytic Number Theory (Vienna, July 18-20, 1996), W. G. Nowak and J. Schoißengeier (eds.), Universität Wien & Universität für Bodenkultur, Wien, 1996, 112-127.
  • [7] A. Ivić, On the ternary additive divisor problem and the sixth moment of the zeta-function, in: Sieve Methods, Exponential Sums, and their Applications in Number Theory, G. R. H. Greaves et al. (eds.), Cambridge Univ. Press, Cambridge, 1996, 205-243.
  • [8] A. Ivić, On the error term for the fourth moment of the Riemann zeta-function, J. London Math. Soc. (2) 60 (1999), 21-32.
  • [9] A. Ivić and Y. Motohashi, A note on the mean value of the zeta and L-functions VII, Proc. Japan Acad. Ser. A 66 (1990), 150-152.
  • [10] A. Ivić and Y. Motohashi, The mean square of the error term for the fourth moment of the zeta-function, Proc. London Math. Soc. (3) 66 (1994), 309-329.
  • [11] A. Ivić and Y. Motohashi, The fourth moment of the Riemann zeta-function, J. Number Theory 51 (1995), 16-45.
  • [12] M. Jutila, Mean value estimates for exponential sums, in: Number Theory (Ulm, 1987), Lecture Notes in Math. 1380, Springer, Berlin, 1989, 120-136.
  • [13] M. Jutila, The fourth moment of Riemann's zeta-function and the additive divisor problem, in: Analytic Number Theory, Proc. of a Conference in Honor of H. Halberstam, Vol. 2, B. C. Berndt et al. (eds.), Birkhäuser, Boston, 1996, 517-536.
  • [14] M. Jutila, Mean values of Dirichlet series via Laplace transforms, in: Proc. Taniguchi International Symposium on Analytic Number Theory, Kyoto, 1996, Y. Motohashi (ed.), Cambridge Univ. Press, Cambridge, 1997, 169-207.
  • [15] A. A. Karacuba and S. M. Voronin, The Riemann Zeta-Function, de Gruyter, Berlin, 1992.
  • [16] N. V. Kuznetsov, Sums of Kloosterman sums and the eighth moment of the Riemann zeta-function, in: Papers presented at the Ramanujan Colloquium, Bombay, 1989, publ. for Tata Institute (Bombay) by Oxford Univ. Press, Oxford, 1989, 57-117.
  • [17] N. N. Lebedev, Special Functions and their Applications, Dover, New York, 1972.
  • [18] Y. Motohashi, Spectral mean values of Maass waveform L-functions, J. Number Theory 42 (1992), 258-284.
  • [19] Y. Motohashi, The fourth power mean of the Riemann zeta-function, in: Proc. of the Amalfi Conference on Analytic Number Theory, 1989, E. Bombieri et al. (eds.), Università di Salerno, Salerno, 1992, 325-344.
  • [20] Y. Motohashi, An explicit formula for the fourth power mean of the Riemann zeta-function, Acta Math. 170 (1993), 181-220.
  • [21] Y. Motohashi, The mean square of Hecke L-series attached to holomorphic cusp forms, RIMS Kyoto Univ. Kokyuroku 886 (1994), 214-227.
  • [22] Y. Motohashi, A relation between the Riemann zeta-function and the hyperbolic Laplacian, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22 (1995), 299-313.
  • [23] Y. Motohashi, The Riemann zeta-function and the non-Euclidean Laplacian, Sugaku Expositions 8 (1995), 59-87.
  • [24] Y. Motohashi, Spectral Theory of the Riemann Zeta-Function, Cambridge Univ. Press, Cambridge, 1997.
  • [25] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1948.
  • [26] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Clarendon Press, Oxford, 1951.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav95z4p305bwm
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