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Lithuanian Mathematical Journal

, Volume 47, Issue 3, pp 311–326 | Cite as

An explicit formula for the square of the Riemann zeta-function in the critical strip

  • Y. Sasaki
Article
  • 70 Downloads

Abstract

In this article, we prove an explicit formula for |ζ(σ + iT)|2, where ζ(s) is the Riemann zeta-function and 1/2 < σ < 1, which is an analogue of Jutila’s formula. Our proof differs from that of Jutila.

Keywords

Riemann zeta-function critical strip Voronoï-type formula 

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References

  1. 1.
    F. V. Atkinson, The mean value of the Riemann zeta-function, Acta Math., 81, 353–376 (1949).CrossRefMathSciNetGoogle Scholar
  2. 2.
    A. Ivić, The Riemann Zeta-Function, Wiley, New York (1985).Google Scholar
  3. 3.
    M. Jutila, Transformation formulae for Dirichlet polynomials, J. Number Theory, 18, 135–156 (1984).zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    K. Matsumoto, The mean square of the Riemann zeta-function in the critical strip, Japanese J. Math., 15, 1–13 (1989).zbMATHGoogle Scholar
  5. 5.
    K. Matsumoto and T. Meurman, The mean square of the Riemann zeta-function in the critical strip II, Acta Arith., 68, 369–382 (1994).zbMATHMathSciNetGoogle Scholar
  6. 6.
    K. Matsumoto and T. Meurman, The mean square of the Riemann zeta-function in the critical strip III, Acta Arith., 64, 357–382 (1993).zbMATHMathSciNetGoogle Scholar
  7. 7.
    A. Oppenheim, Some identities in the theory of numbers, in: Proc. London Math. Soc. (2), vol. 26 (1927), pp. 295–350.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Y. Sasaki
    • 1
  1. 1.Graduate School of MathematicsNagoya UniversityChikusa-ku, NagoyaJapan

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