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

Kohji Matsumoto; Tom Meurman

Acta Arithmetica (1993)

  • Volume: 64, Issue: 4, page 357-382
  • ISSN: 0065-1036

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Kohji Matsumoto, and Tom Meurman. "The mean square of the Riemann zeta-function in the critical strip III." Acta Arithmetica 64.4 (1993): 357-382. <http://eudml.org/doc/206557>.

@article{KohjiMatsumoto1993,
author = {Kohji Matsumoto, Tom Meurman},
journal = {Acta Arithmetica},
keywords = {critical strip; Riemann zeta-function; Voronoi formula; Omega theorem; error term; asymptotic formula; Atkinson's formula; mean square},
language = {eng},
number = {4},
pages = {357-382},
title = {The mean square of the Riemann zeta-function in the critical strip III},
url = {http://eudml.org/doc/206557},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Kohji Matsumoto
AU - Tom Meurman
TI - The mean square of the Riemann zeta-function in the critical strip III
JO - Acta Arithmetica
PY - 1993
VL - 64
IS - 4
SP - 357
EP - 382
LA - eng
KW - critical strip; Riemann zeta-function; Voronoi formula; Omega theorem; error term; asymptotic formula; Atkinson's formula; mean square
UR - http://eudml.org/doc/206557
ER -

References

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  1. [1] F. V. Atkinson, The mean-value of the Riemann zeta function, Acta Math. 81 (1949), 353-376. Zbl0036.18603
  2. [2] K. Chandrasekharan and R. Narasimhan, Approximate functional equations for a class of zeta-functions, Math. Ann. 152 (1963), 30-64. Zbl0116.27001
  3. [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. [4] D. R. Heath-Brown, The mean value theorem for the Riemann zeta-function, Mathematika 25 (1978), 177-184. Zbl0387.10023
  5. [5] A. Ivić, The Riemann Zeta-Function. The Theory of the Riemann Zeta-Function with Applications, Wiley, 1985. Zbl0556.10026
  6. [6] A. Ivić, Mean Values of the Riemann Zeta Function, Lectures on Math. 82, Tata Inst. Fund. Res., Springer, 1991. 
  7. [7] A. Ivić, La valeur moyenne de la fonction zêta de Riemann, Sém. Théorie des Nombres 1990/91, Université Orsay, Paris, to appear. 
  8. [8] M. Jutila, A Method in the Theory of Exponential Sums, Lectures on Math. 80, Tata Inst. Fund. Res., Springer, 1987. 
  9. [9] K. Matsumoto, The mean square of the Riemann zeta-function in the critical strip, Japan. J. Math. 15 (1989), 1-13. Zbl0684.10035
  10. [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. [11] T. Meurman, A generalization of Atkinson's formula to L-functions, Acta Arith. 47 (1986), 351-370. Zbl0561.10019
  12. [12] T. Meurman, On the mean square of the Riemann zeta-function, Quart. J. Math. Oxford (2) 38 (1987), 337-343. Zbl0624.10032
  13. [13] T. Meurman, A simple proof of Voronoï's identity, to appear. Zbl0788.11042
  14. [14] T. Meurman, Voronoï’s identity for the Riesz mean of σ α ( n ) , unpublished manuscript, 24 pp. 
  15. [15] Y. Motohashi, The mean square of ζ(s) off the critical line, unpublished manuscript, 11 pp. 
  16. [16] A. Oppenheim, Some identities in the theory of numbers, Proc. London Math. Soc. (2) 26 (1927), 295-350. Zbl53.0150.02
  17. [17] E. Preissmann, Sur la moyenne quadratique de la fonction zêta de Riemann, preprint. 
  18. [18] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford Univ. Press, Oxford 1951. Zbl0042.07901

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