Several problems and results on mean values of are discussed. These include mean values of and the fourth moment of for .
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 .
Keywords: Riemann zeta-function, mean values, asymptotic formulas
@article{JTNB_1996__8_1_101_0,
author = {Aleksandar Ivi\'c},
title = {Some problems on mean values of the {Riemann} zeta-function},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {101--123},
year = {1996},
publisher = {Universit\'e Bordeaux I},
volume = {8},
number = {1},
doi = {10.5802/jtnb.159},
zbl = {0858.11045},
mrnumber = {1399949},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.159/}
}
TY - JOUR AU - Aleksandar Ivić TI - Some problems on mean values of the Riemann zeta-function JO - Journal de théorie des nombres de Bordeaux PY - 1996 SP - 101 EP - 123 VL - 8 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.159/ DO - 10.5802/jtnb.159 LA - en ID - JTNB_1996__8_1_101_0 ER -
%0 Journal Article %A Aleksandar Ivić %T Some problems on mean values of the Riemann zeta-function %J Journal de théorie des nombres de Bordeaux %D 1996 %P 101-123 %V 8 %N 1 %I Université Bordeaux I %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.159/ %R 10.5802/jtnb.159 %G en %F JTNB_1996__8_1_101_0
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
[1] , On the frequency of Titchmarsh's phenomenon for ζ(s) IV, Hardy-Ramanujan J.9 (1986), 1-10. | Zbl
[2] , and , The mean square of the Riemann zeta-function on the line σ = 1, L'Enseignement Mathématique 38 (1992), 13-25. | Zbl
[3] and , Power mean values of the Riemann zeta-function, Mathematika 29 (1982), 202-212. | MR | Zbl
[4] , The Riemann zeta-function, John Wiley & Sons, New York, (1985). | MR | Zbl
[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
[6] , The moments of the zeta-function on the line σ =1, Nagoya Math. J. 135 (1994), 113-129. | Zbl
[7] and , Mean values of certain zeta-functions on the critical line, Litovskij Mat. Sbornik 29 (1989), 701-714. | MR | Zbl
[8] and , 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 | Zbl
[9] , Distribution theorems for L-functions, Longman Scientific & Technical, Essex (1986). | MR | Zbl
[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
[11] , The mean square of the Riemann zeta-function in the critical strip, Japan. J. Math. 13 (1989), 1-13. | MR | Zbl
[12] and , 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 | Zbl
[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 | Zbl
[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 | Zbl
[15] , A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math. 31 (1980), 161-170. | MR | Zbl
[16] , The theory of the Riemann zeta-function (2nd ed.), Oxford, Clarendon Press, (1986). | MR | Zbl
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