The mean square of the Riemann zeta-function in the critical strip III

• Autorzy: Kohji Matsumoto , Tom Meurman
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 64
• Numer: 4
• Strony: 357-382

Daty

wydano

1993

otrzymano

1992-12-22

Twórcy

autor

Kohji Matsumoto

• Department of Mathematics, Faculty of Education, Iwate University, Morioka 020, Japan

autor

Tom Meurman

• Department of Mathematics, University of Turku, SF-20500 Turku, Finland

Bibliografia

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• [2] K. Chandrasekharan and R. Narasimhan, Approximate functional equations for a class of zeta-functions, Math. Ann. 152 (1963), 30-64.
• [3] J. L. Hafner, On the representation of the summatory functions of a class of arithmetical functions, in: Analytic Number Theory, M. I. Knopp (ed.), Lecture Notes in Math. 899, Springer, 1981, 148-165.
• [4] D. R. Heath-Brown, The mean value theorem for the Riemann zeta-function, Mathematika 25 (1978), 177-184.
• [5] A. Ivić, The Riemann Zeta-Function. The Theory of the Riemann Zeta-Function with Applications, Wiley, 1985.
• [6] A. Ivić, Mean Values of the Riemann Zeta Function, Lectures on Math. 82, Tata Inst. Fund. Res., Springer, 1991.
• [7] A. Ivić, La valeur moyenne de la fonction zêta de Riemann, Sém. Théorie des Nombres 1990/91, Université Orsay, Paris, to appear.
• [8] M. Jutila, A Method in the Theory of Exponential Sums, Lectures on Math. 80, Tata Inst. Fund. Res., Springer, 1987.
• [9] K. Matsumoto, The mean square of the Riemann zeta-function in the critical strip, Japan. J. Math. 15 (1989), 1-13.
• [10] K. Matsumoto and T. Meurman, The mean square of the Riemann zeta-function in the critical strip II, Journées Arithmétiques de Genève 1991, Astérisque 209 (1992), 265-274.
• [11] T. Meurman, A generalization of Atkinson's formula to L-functions, Acta Arith. 47 (1986), 351-370.
• [12] T. Meurman, On the mean square of the Riemann zeta-function, Quart. J. Math. Oxford (2) 38 (1987), 337-343.
• [13] T. Meurman, A simple proof of Voronoï's identity, to appear.
• [14] T. Meurman, Voronoï's identity for the Riesz mean of $σ_α(n)$, unpublished manuscript, 24 pp.
• [15] Y. Motohashi, The mean square of ζ(s) off the critical line, unpublished manuscript, 11 pp.
• [16] A. Oppenheim, Some identities in the theory of numbers, Proc. London Math. Soc. (2) 26 (1927), 295-350.
• [17] E. Preissmann, Sur la moyenne quadratique de la fonction zêta de Riemann, preprint.
• [18] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford Univ. Press, Oxford 1951.