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ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Department of Mathematics, Faculty of Education, Iwate University, Morioka 020, Japan
  2. Department of Mathematics, University of Turku, SF-20500 Turku, Finland

Bibliography

  1. F. V. Atkinson, The mean-value of the Riemann zeta function, Acta Math. 81 (1949), 353-376.
  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 T. Meurman, Voronoï's identity for the Riesz mean of σα(n), unpublished manuscript, 24 pp.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 Y. Motohashi, The mean square of ζ(s) off the critical line, unpublished manuscript, 11 pp.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.
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  18. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford Univ. Press, Oxford 1951.
Acta Arithmetica
1993/64/4
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Pages:
357-382
Main language of publication
English
Received
1992-12-22
Published
1993
Exact and natural sciences