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The moments of the zeta-function on the line σ = 1

Published online by Cambridge University Press:  22 January 2016

Aleksandar Ivić
Aleksandar Ivić*
Affiliation:
Katedra Matematike RGF-a, Universiteta u Beogradu, Djušina 7, 11000 Beograd, Serbia (Yugoslavia)
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The evaluation of the integral

(1.1)

represents one of the fundamental problems of the theory of the Riemann zeta-function (see [4] for a comprehensive account). In view of the functional equation

it is clear that one has to distinguish between the following three principal cases:

  • a) σ = 1/2 (“the critical line”),

  • b) 1/2 < σ < 1 (“the critical strip”),

  • c) σ = 1.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 135 , September 1994 , pp. 113 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

[1] Balasubramanian, R., Ivic, A. and Ramachandra, K., The mean square of the Riemann zeta-function on the line σ=1, L’Enseignement Math., 38 (1992), 13–25.Google Scholar
[2] Dixon, R. D., On a generalized divisor problem, J. Indian Math. Soc, 28 (1964), 187–196.Google Scholar
[3] Ivic, A., The Riemann zeta-function, John Wiley & Sons, New York, 1985.Google Scholar
[4] Ivic, A., Mean values of the Riemann zeta-function, Tata Institute Lecture Notes, 82, Bombay, 1991 (distr. by Springer Verlag, Berlin etc.).Google Scholar
[5] Nakaya, H., The generalized divisor problem and the Riemann hypothesis, Nagoya Math. J., 122(1991), 149–159.Google Scholar
[6] Titchmarsh, E. C., The theory of the Riemann zeta-function (2nd ed. rev. by Heath-Brown, D. R.), Clarendon Press, Oxford, 1986.Google Scholar