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On the moments of the Riemann zeta-function near the critical line

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References

  1. F. V. Atkinson, The mean value of the Riemann zeta-function,Acta Math.,81, 353–376 (1949).

    MATH  MathSciNet  Google Scholar 

  2. J. B. Conrey and A. Ghosh, On mean values of the zeta-function,Mathematika,31, 159–161 (1984).

    MathSciNet  Google Scholar 

  3. R. M. Gabriel, Some results concerning the integrals of moduli of regular functions along certain curves,J. London Math. Soc.,2, 112–117 (1927).

    MATH  Google Scholar 

  4. A. Good, Ein Ω-Result für quadratishe Mittel der Riemannschen Zetafunktion auf der kritische Linie,Invent. Math.,41, 233–251 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  5. 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 

  6. D. R. Heath-Brown, Fractional moments of the Riemann zeta-function,J. London Math. Soc. (2),24, 65–78 (1981).

    MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  8. D. R. Heath-Brown, Fractional moments of the Riemann zeta-function. II,Quart. J. Math. Oxford (2),44, 185–197 (1993).

    MATH  MathSciNet  Google Scholar 

  9. 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 

  10. A. Ivič,The Riemann Zeta-Function, John Wiley and Sons, New York (1985).

    Google Scholar 

  11. A. Ivič,Mean values of the Riemann zeta-function, Lecture Note Ser. 82, Tata Institute of Fundamental Research, Bombay (1991).

    Google Scholar 

  12. A. Ivič and K. Matsumoto, On the error term in the mean square formula for the Riemann zeta-function in the critical strip (1994) (preprint).

  13. D. Joyner,Distribution Theorems of L-functions, Longman Scientific, Harlow (1986).

    Google Scholar 

  14. M. Jutila, On the value distribution of the zeta-function on the critical line,Bull. London Math. Soc.,15, 513–518 (1983).

    MATH  MathSciNet  Google Scholar 

  15. A. Laurinčikas, A limit theorem for the Riemann zeta-function close to the critical line,Mat. Sb.,135 (177), No 1, 3–11 (1988).

    Google Scholar 

  16. A. Laurinčikas, A limit theorem for the Riemann zeta-function close to the critical line. II,Mat. Sb.,180, No 6, 733–749 (1989).

    Google Scholar 

  17. A. Laurinčikas, The Atkinson formula near the critical line, in:New Trends in Probab. and Statist. Vol. 2, VSP/TEV (1992), pp. 335–354

  18. A. Laurinčikas, Once more on the function σa(m),Lith. Math. J.,32, 78–90 (1992).

    Google Scholar 

  19. A. Laurinčikas, The Atkinson formula near the critical line. II,Lith. Math. J.,33, 234–242 (1993).

    Google Scholar 

  20. A. Laurinčikas, The Atkinson formula forL-functions near the critical line,Lith. Math. J.,33, 337–351 (1993).

    Google Scholar 

  21. A. Laurinčikas, On limit theorems for the Riemann zeta-function in some spaces, in:Proceedings of sixth Vilnius Conference on Prob. Theory and Math. Stat., VSP/TEV (1994), pp. 457–483.

  22. A. Laurinčikas, A remark on the Conrey-Ghosh theorem,Liet. Mat. Rinkinys (to appear).

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

    MATH  MathSciNet  Google Scholar 

  24. K. Matsumoto and T. Meurman, The mean square of the Riemann zeta-function in the critical strip. III,Acta Arith.,64, 357–382 (1993).

    MathSciNet  Google Scholar 

  25. K. Matsumoto, On the functionE σ(T),Sūrikaiseki Kenkyūsho Kōkyūoku,886, 10–28 (1994).

    MATH  Google Scholar 

  26. H. L. Montgomery and R. C. Vaughan, Hilbert's inequality,J. London Math. Soc. (2),8, 73–82 (1974).

    MathSciNet  Google Scholar 

  27. K. Ramachandra, Some remarks on the mean value of the Riemann zeta-function and other Dirichlet series. I,Hardy-Ramanujan J.,1, 1–15 (1978).

    MATH  MathSciNet  Google Scholar 

  28. K. Ramachandra, Some remarks on the mean value of the Riemann zeta-function and other Dirichlet series. III,Ann. Acad. Sci. Fenn. Ser. A. I,5, 145–158 (1980).

    MATH  MathSciNet  Google Scholar 

  29. K. Ramachandra, A brief summary of some results in the analytic theory of numbers. II,Lect. Notes in Math.,938, 106–222 (1982).

    MATH  MathSciNet  Google Scholar 

  30. E. C. Titchmarsh,The Theory of the Riemann Zeta-Function, Clarendon Press, Oxford (1951).

    Google Scholar 

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Additional information

This paper is a communication which was presented at the International Congress of Mathematicians in Zürich, 3–11 August 1994.

The research described in this publication was partially supported by Grant N LAC000 from the International Science Foundation.

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 3, pp. 332–359, July–September, 1995.

Translated by A. Laurinčikas

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Laurinčikas, A. On the moments of the Riemann zeta-function near the critical line. Lith Math J 35, 262–283 (1995). https://doi.org/10.1007/BF02350362

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