Sur les moments d'une fonction additive
Hildebrand, Adolph
Annales de l'Institut Fourier, Tome 33 (1983), p. 1-22 / Harvested from Numdam
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On donne des estimations précises pour les quantités 1 X∑ n≤X |f(n)-A| β , où f est une fonction arithmétique additive et A,β>0 et x≥1 sont des nombres réels.

We give precise estimations for the quantities 1 X∑ n≤X |f(n)-A| β , where f is an additive arithmetical function and A,β>0 and x≥1 are real numbers.

@article{AIF_1983__33_3_1_0,
     author = {Hildebrand, Adolph},
     title = {Sur les moments d'une fonction additive},
     journal = {Annales de l'Institut Fourier},
     volume = {33},
     year = {1983},
     pages = {1-22},
     doi = {10.5802/aif.928},
     mrnumber = {85c:11067},
     zbl = {0486.10043},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1983__33_3_1_0}
}

Hildebrand, Adolph. Sur les moments d'une fonction additive. Annales de l'Institut Fourier, Tome 33 (1983) pp. 1-22. doi : 10.5802/aif.928. http://gdmltest.u-ga.fr/item/AIF_1983__33_3_1_0/

[1] P.D.T.A. Elliott, High power analogues of the Turán-Kubilius inequality and an application to number theory, Can. J. Math., 32 (1980), 893-907. | MR 81m:10082 | Zbl 0444.10051

[2] P.D.T.A. Elliott, Probabilistic number theory I, Springer, New York - Heidelberg - Berlin, 1979. | MR 82h:10002a | Zbl 0431.10029

[3] P. Erdös et I.Z. Ruzsa, On the small sieve I, J. Number Th., 12 (1980), 385-394. | Zbl 0435.10028

[4] A. Hildebrand et J. Spilker, Eine Charakterisierung der additiven, fastgeraden Funktionen, Manuscripta Math., 32 (1980), 213-230. | MR 82g:10066 | Zbl 0446.10041

[5] I.Z. Ruzsa, On the concentration of additive functions, Acta Math. Acad. Sci. Hung., 36 (1980), 215-232. | MR 82j:10088 | Zbl 0471.10034

[6] I.Z. Ruzsa, On the variance of additive functions, Preprint. | Zbl 0519.10045

[7] I.Z. Ruzsa, Generalized moments of additive functions, Preprint. | Zbl 0524.10042

[8] D. Wolke, Das Selbergsche Sieb für Zahlenthetische Funktionen I, Arch. Math., 24 (1973), 632-639. | MR 49 #2618 | Zbl 0278.10041