Multiplicative Functions in Short Intervals
Canadian journal of mathematics, Tome 39 (1987) no. 3, pp. 646-672

Voir la notice de l'article provenant de la source Cambridge University Press

A central problem in probabilistic number theory is to evaluate asymptotically the partial sums of multiplicative functions f and, in particular, to find conditions for the existence of the “mean value” 1.1 In the last two decades considerable progress has been made on this problem, and the results obtained are very satisfactory.
Hildebrand, Adolf. Multiplicative Functions in Short Intervals. Canadian journal of mathematics, Tome 39 (1987) no. 3, pp. 646-672. doi: 10.4153/CJM-1987-032-6
@article{10_4153_CJM_1987_032_6,
     author = {Hildebrand, Adolf},
     title = {Multiplicative {Functions} in {Short} {Intervals}},
     journal = {Canadian journal of mathematics},
     pages = {646--672},
     year = {1987},
     volume = {39},
     number = {3},
     doi = {10.4153/CJM-1987-032-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-032-6/}
}
TY  - JOUR
AU  - Hildebrand, Adolf
TI  - Multiplicative Functions in Short Intervals
JO  - Canadian journal of mathematics
PY  - 1987
SP  - 646
EP  - 672
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-032-6/
DO  - 10.4153/CJM-1987-032-6
ID  - 10_4153_CJM_1987_032_6
ER  - 
%0 Journal Article
%A Hildebrand, Adolf
%T Multiplicative Functions in Short Intervals
%J Canadian journal of mathematics
%D 1987
%P 646-672
%V 39
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-032-6/
%R 10.4153/CJM-1987-032-6
%F 10_4153_CJM_1987_032_6

[1] 1. Babu, G. J., Probabilistic methods in the theory of arithmetical functions, Macmillan Lectures in Mathematics, New Delhi (1978). Google Scholar

[2] 2. Babu, G. J., On the distribution of arithmetic functions, Acta Arith. 29 (1976), 97–104. Google Scholar

[3] 3. Babu, G. J., On the mean values and distributions of arithmetic functions, Acta Arith. 40 (1981), 63–77. Google Scholar

[4] 4. Delange, H., Sur les fonctions arithmétiques multiplicatives, Ann. Scient. Ec. Norm. Sup. 75 (1961), 273–304. Google Scholar

[5] 5. Elliott, P. D. T. A., Probabilistic number theory I, II (Springer, New York, 1979, 1980). Google Scholar | DOI

[6] 6. Elliott, P. D. T. A., Arithmetic functions and integer products (Springer, New York, 1985). Google Scholar | DOI

[7] 7. Halá;sz, G., Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hung. 19 (1968), 365–403. Google Scholar

[8] 8. Halá;sz, G., On the distribution of additive arithmetic functions. Acta Arith. 27 (1975), 143–152. Google Scholar

[9] 9. Halberstam, H. and Richert, H.-E., On a result of R. R. Hall, J. Number Theory 11 (1979), 76–89. Google Scholar

[10] 10. Hildebrand, A., On Wirsing's mean value theorem for multiplicative functions, Bull. London Math Soc. 18 (1986), 147–152. Google Scholar

[11] 11. Huxley, M. N., On the difference between consecutive primes, Invent. Math. 15 (1972), 164–170. Google Scholar

[12] 12. Montgomery, H. L., A note on mean values of multiplicative functions, Preprint. Mittag-Leffler Institute (1978). Google Scholar

[13] 13. Motohashi, Y., On the sum of the Môbiusfunction in a short segment, Proc. Japan Acad. 52 (1976), 477–479. Google Scholar

[14] 14. Ramachandra, K., Some problems of analytic number theory, Acta Arith. 31 (1976), 313–323. Google Scholar

[15] 15. Shiu, P., A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Ang. Math. 313 (1980), 161–170. Google Scholar

[16] 16. Wirsing, E., Das asymptotische Verhalten von Summen über multiplikative Funktionen II, Acta Math. Acad. Sci. Hung. 18 (1967), 411–467. Google Scholar

Cité par Sources :