Some problems on mean values of the Riemann zeta-function

Aleksandar Ivić

Journal de théorie des nombres de Bordeaux (1996)

  • Volume: 8, Issue: 1, page 101-123
  • ISSN: 1246-7405

Abstract

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Several problems and results on mean values of ζ ( s ) are discussed. These include mean values of | ζ ( 1 2 + i t ) | and the fourth moment of | ζ ( σ + i t ) | for 1 / 2 < σ < 1 .

How to cite

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Ivić, Aleksandar. "Some problems on mean values of the Riemann zeta-function." Journal de théorie des nombres de Bordeaux 8.1 (1996): 101-123. <http://eudml.org/doc/247820>.

@article{Ivić1996,
abstract = {Several problems and results on mean values of $\zeta (s)$ are discussed. These include mean values of $|\zeta (\frac\{1\}\{2\} + it)|$ and the fourth moment of $|\zeta (\sigma + it)|$ for $1/2 &lt; \sigma &lt; 1$.},
author = {Ivić, Aleksandar},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Riemann zeta-function; mean values; asymptotic formulas; mean values of the Riemann zeta-function; fractional moments; fourth power moment; error term; asymptotic formula},
language = {eng},
number = {1},
pages = {101-123},
publisher = {Université Bordeaux I},
title = {Some problems on mean values of the Riemann zeta-function},
url = {http://eudml.org/doc/247820},
volume = {8},
year = {1996},
}

TY - JOUR
AU - Ivić, Aleksandar
TI - Some problems on mean values of the Riemann zeta-function
JO - Journal de théorie des nombres de Bordeaux
PY - 1996
PB - Université Bordeaux I
VL - 8
IS - 1
SP - 101
EP - 123
AB - Several problems and results on mean values of $\zeta (s)$ are discussed. These include mean values of $|\zeta (\frac{1}{2} + it)|$ and the fourth moment of $|\zeta (\sigma + it)|$ for $1/2 &lt; \sigma &lt; 1$.
LA - eng
KW - Riemann zeta-function; mean values; asymptotic formulas; mean values of the Riemann zeta-function; fractional moments; fourth power moment; error term; asymptotic formula
UR - http://eudml.org/doc/247820
ER -

References

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  1. [1] R. Balasubramanian, On the frequency of Titchmarsh's phenomenon for ζ(s) IV, Hardy-Ramanujan J.9 (1986), 1-10. Zbl0662.10030
  2. [2] R. Balasubramanian, A. Ivić and K. Ramachandra, The mean square of the Riemann zeta-function on the line σ = 1, L'Enseignement Mathématique38 (1992), 13-25. Zbl0753.11028
  3. [3] J.-M. Deshouillers and H. Iwaniec, Power mean values of the Riemann zeta-function, Mathematika29 (1982), 202-212. Zbl0506.10032MR696876
  4. [4] A. Ivić, The Riemann zeta-function, John Wiley & Sons, New York, (1985). Zbl0556.10026MR792089
  5. [5] A. Ivić, The mean values of the Riemann zeta-function, Tata Institute for Fundamental Research LN's82, Bombay1991 (distr. by Springer Verlag, Berlin etc., 1992). MR1230387
  6. [6] A. Ivić, The moments of the zeta-function on the line σ =1, Nagoya Math. J.135 (1994), 113-129. Zbl0804.11048
  7. [7] A. Ivić and A. Perelli, Mean values of certain zeta-functions on the critical line, Litovskij Mat. Sbornik29 (1989), 701-714. Zbl0706.11049MR1060670
  8. [8] A. Ivić and Y. Motohashi, The mean square of the error term for the fourth moment of the zeta-function, Proc. London Math. Soc. (3) 69 (1994), 309-329. Zbl0805.11060MR1281967
  9. [9] D. Joyner, Distribution theorems for L-functions, Longman Scientific & Technical, Essex (1986). Zbl0609.10032MR865983
  10. [10] A. Laurinčinkas, The limit theorem for the Riemann zeta-function on the critical line I, (Russian), Litovskij Mat. Sbornik27 (1987), 113-132 and II ibid.27 (1987), 459-500. Zbl0641.10031
  11. [11] K. Matsumoto, The mean square of the Riemann zeta-function in the critical strip, Japan. J. Math.13 (1989), 1-13. Zbl0684.10035MR1053629
  12. [12] K. Matsumoto and T. Meurman, The mean square of the Riemann zeta-function in the critical strip II, Acta Arith.68 (1994), 369-382; III, Acta Arith.64 (1993), 357-382. Zbl0788.11035MR1307453
  13. [13] K. Ramachandra, Some remarks on the mean value of the Riemann zeta-function and other Dirichlet series IV, J. Indian Math. Soc.60 (1994), 107-122. Zbl0882.11049MR1292129
  14. [14] K. Ramachandra, Lectures on the mean-value and omega-theorems for the Riemann zeta-function, LNs 85, Tata Institute of Fundamental Research, Bombay1995 (distr. by Springer Verlag, Berlin etc.). Zbl0845.11003MR1332493
  15. [15] P. Shiu, A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math.31 (1980), 161-170. Zbl0412.10030MR552470
  16. [16] E.C. Titchmarsh, The theory of the Riemann zeta-function (2nd ed.), Oxford, Clarendon Press, (1986). Zbl0601.10026MR882550

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