Skip to main content
Log in

The asymptotic behavior of the second power moment of the Riemann zeta-function in the critical strip

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. S. W. Graham and G. Kolesnik,Van der Corput's Method for Exponential Sums, London Mathematical Society Lecture Notes 126, Cambridge University Press (to appear).

  2. G. H. Hardy and J. E. Littlewood, Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes,Acta Math.,41, 119–196 (1918).

    Google Scholar 

  3. D. R. Heath-Brown, The fourth power moment of the Riemann zeta-function,Proc. London Math. Soc. (3),38, 385–422 (1979).

    MATH  MathSciNet  Google Scholar 

  4. D. R. Heath-Brown and M. N. Huxley, Exponential sums with a difference,Proc. London Math. Soc. (3),61, 227–250 (1990).

    MathSciNet  Google Scholar 

  5. A. E. Ingham, Mean value theorems in the theory of the Riemann zeta-function,Proc. London Math. Soc. (2),27, 273–300 (1926).

    Google Scholar 

  6. A. Ivič,The Riemann Zeta-Function, Wiley, New York (1985).

    Google Scholar 

  7. A. Ivič,Mean Values of the Riemann Zeta-Function, Lecture Note Ser. 82, Tata Inst. Fund. Res., Bombay, distributed by Springer (1991).

  8. A. Ivič and K. Matsumoto, On the error term in the mean square formula for the Riemann zeta-function in the critical strip (in press).

  9. A. Laurinčikas, The Atkinson formula near the critical line, in:Proc. of the Inter. Conf. in Honour of J. Kubilius, Vol. 2, Palanga, Lihuania, 24–28 Sept., 1991.

  10. K. Matsumoto, The mean square of the Riemann zeta-function in the critical strip,Jpn. J. Math,15, 1–13 (1989).

    MATH  Google Scholar 

  11. K. Matsumoto,On the Function E σ(T), Analytic number theory, RIMS Kokyuroku 886, September, 1994, Kyoto University, Kyoto, Japan.

    Google Scholar 

  12. Y. Motohashi, The mean square ofσ(s) of the critical line, Unpublished manuscript (1990).

  13. E. A. Whittaker and G. N. Watson,A Course of Modern Analysis Cambridge University Press (1969).

Download references

Authors

Additional information

The research described in this paper was partially supported by grant No. LI2100 from the Joint Program of the Lithuanian Government and the International Sciences Foundation.

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 3, pp. 315–331, July–September, 1995.

Translated by A. Kačenas

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kačénas, A. The asymptotic behavior of the second power moment of the Riemann zeta-function in the critical strip. Lith Math J 35, 249–261 (1995). https://doi.org/10.1007/BF02350361

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02350361

Keywords

Navigation