On s’intéresse à des problèmes et des résultats relatifs aux valeurs moyennes de la fonction . On étudie en particulier des valeurs moyennes de , ainsi que le moment d’ordre de pour .
Several problems and results on mean values of are discussed. These include mean values of and the fourth moment of for .
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}, zbl = {0858.11045}, mrnumber = {1399949}, language = {en}, url = {http://www.numdam.org/item/JTNB_1996__8_1_101_0/} }
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 DA - 1996/// SP - 101 EP - 123 VL - 8 IS - 1 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1996__8_1_101_0/ UR - https://zbmath.org/?q=an%3A0858.11045 UR - https://www.ams.org/mathscinet-getitem?mr=1399949 LA - en ID - JTNB_1996__8_1_101_0 ER -
Ivić, Aleksandar. 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. http://www.numdam.org/item/JTNB_1996__8_1_101_0/
[1] On the frequency of Titchmarsh's phenomenon for ζ(s) IV, Hardy-Ramanujan J.9 (1986), 1-10. | Zbl 0662.10030
,[2] The mean square of the Riemann zeta-function on the line σ = 1, L'Enseignement Mathématique 38 (1992), 13-25. | Zbl 0753.11028
, and ,[3] Power mean values of the Riemann zeta-function, Mathematika 29 (1982), 202-212. | MR 696876 | Zbl 0506.10032
and ,[4] The Riemann zeta-function, John Wiley & Sons, New York, (1985). | MR 792089 | Zbl 0556.10026
,[5] 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] The moments of the zeta-function on the line σ =1, Nagoya Math. J. 135 (1994), 113-129. | Zbl 0804.11048
,[7] Mean values of certain zeta-functions on the critical line, Litovskij Mat. Sbornik 29 (1989), 701-714. | MR 1060670 | Zbl 0706.11049
and ,[8] 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
and ,[9] Distribution theorems for L-functions, Longman Scientific & Technical, Essex (1986). | MR 865983 | Zbl 0609.10032
,[10] 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] 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] 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
and ,[13] 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] 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] A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math. 31 (1980), 161-170. | MR 552470 | Zbl 0412.10030
,[16] The theory of the Riemann zeta-function (2nd ed.), Oxford, Clarendon Press, (1986). | MR 882550 | Zbl 0601.10026
,