Some problems on mean values of the Riemann zeta-function
Journal de Théorie des Nombres de Bordeaux, Tome 8 (1996) no. 1, pp. 101-123.

On s’intéresse à des problèmes et des résultats relatifs aux valeurs moyennes de la fonction ζ(s). On étudie en particulier des valeurs moyennes de |ζ(1 2+it)|, ainsi que le moment d’ordre 4 de |ζ(σ+it)| pour 1/2<σ<1.

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

DOI : https://doi.org/10.5802/jtnb.159
Classification : Primary 11M06
Mots clés : Riemann zeta-function, mean values, asymptotic formulas
@article{JTNB_1996__8_1_101_0,
     author = {Ivi\'c, Aleksandar},
     title = {Some problems on mean values of the {Riemann} zeta-function},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {101--123},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {1},
     year = {1996},
     doi = {10.5802/jtnb.159},
     zbl = {0858.11045},
     mrnumber = {1399949},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.159/}
}
Aleksandar Ivić. Some problems on mean values of the Riemann zeta-function. Journal de Théorie des Nombres de Bordeaux, Tome 8 (1996) no. 1, pp. 101-123. doi : 10.5802/jtnb.159. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.159/

[1] R. Balasubramanian, On the frequency of Titchmarsh's phenomenon for ζ(s) IV, Hardy-Ramanujan J.9 (1986), 1-10. | Zbl 0662.10030

[2] R. Balasubramanian, A. Ivić and K. Ramachandra, The mean square of the Riemann zeta-function on the line σ = 1, L'Enseignement Mathématique 38 (1992), 13-25. | Zbl 0753.11028

[3] J.-M. Deshouillers and H. Iwaniec, Power mean values of the Riemann zeta-function, Mathematika 29 (1982), 202-212. | MR 696876 | Zbl 0506.10032

[4] A. Ivić, The Riemann zeta-function, John Wiley & Sons, New York, (1985). | MR 792089 | Zbl 0556.10026

[5] A. Ivić, The mean values of the Riemann zeta-function, Tata Institute for Fundamental Research LN's 82, Bombay 1991 (distr. by Springer Verlag, Berlin etc., 1992). | MR 1230387

[6] A. Ivić, The moments of the zeta-function on the line σ =1, Nagoya Math. J. 135 (1994), 113-129. | Zbl 0804.11048

[7] A. Ivić and A. Perelli, Mean values of certain zeta-functions on the critical line, Litovskij Mat. Sbornik 29 (1989), 701-714. | MR 1060670 | Zbl 0706.11049

[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. | MR 1281967 | Zbl 0805.11060

[9] D. Joyner, Distribution theorems for L-functions, Longman Scientific & Technical, Essex (1986). | MR 865983 | Zbl 0609.10032

[10] A. Laurinčinkas, The limit theorem for the Riemann zeta-function on the critical line I, (Russian), Litovskij Mat. Sbornik 27 (1987), 113-132 and II ibid. 27 (1987), 459-500. | Zbl 0641.10031

[11] K. Matsumoto, The mean square of the Riemann zeta-function in the critical strip, Japan. J. Math. 13 (1989), 1-13. | MR 1053629 | Zbl 0684.10035

[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. | MR 1307453 | Zbl 0788.11035

[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. | MR 1292129 | Zbl 0882.11049

[14] K. Ramachandra, Lectures on the mean-value and omega-theorems for the Riemann zeta-function, LNs 85, Tata Institute of Fundamental Research, Bombay 1995 (distr. by Springer Verlag, Berlin etc.). | MR 1332493 | Zbl 0845.11003

[15] P. Shiu, A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math. 31 (1980), 161-170. | MR 552470 | Zbl 0412.10030

[16] E.C. Titchmarsh, The theory of the Riemann zeta-function (2nd ed.), Oxford, Clarendon Press, (1986). | MR 882550 | Zbl 0601.10026