Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF

Book Information

Author(s): Jean-Loup Mauclaire
Title: Intégration et théorie des nombres
Additional book information: preface by S. Iyanagi. Hermann, Paris, 1986, xi + 152 pp., 160F. ISBN 2-7056-6035-6


References:

1.
H. Daboussi, Caractérisation des fonctions multiplicatives p. p. B, Ann. Inst. Fourier (Grenoble) 30 (1980), 141-166. MR 597021
2.
H. Daboussi, Sur les fonctions multiplicatives ayant une valeur moyenne non nulle, Bull. Soc. Math. France 109 (1981), 183-205. MR 623788
3.
H. Daboussi and H. Delange, On multiplicative arithmetical functions whose modulus does not exceed one, J. London Math. Soc. (2) 26 (1982), 245-264. MR 675168
4.
H. Davenport, Multiplicative number theory, second edition, revised by H. Montgomery, Graduate Texts in Math., no. 74, Springer-Verlag, Berlin, New York, Heidelberg, 1980. MR 606931
5.
H. Delange, Sur les fonctions arithmétiques multiplicatives, Ann. Sci. École Norm. Sup. 78 (1961), 273-304. MR 169829
6.
P. G. L. Dirichlet, Über die Bestimmung der mittleren Werthe in der Zahlentheorie, Abh. Akad. Berlin (1849), 69-83; see: Werke, Vol. 2, VI, Reimer, Berlin, 1897.
7.
H. M. Edwards, Riemann's zeta function, Academic Press, New York, 1974. MR 466039
8.
P. D. T. A. Elliott, A mean-value theorem for multiplicative functions, Proc. London Math. Soc. 31 (1975), 418-438. MR 387220
9.
P. D. T. A. Elliott, Mean-value theorems for multiplicative functions bounded in mean α-power, α > 1, J. Austral. Math. Soc. Ser. A 29 (1980), 177-205. MR 566285
10.
P. D. T. A. Elliott, Probabilistic number theory. I: Mean-value theorems, II: Central limit theorems, Grundlehren Math. Wiss. 234, 240, Springer-Verlag, Berlin, New York, 1979, 1980. MR 551361
11.
P. D. T. A. Elliott, High-power analogues of the Turán-Kubilius inequality, and an application to number theory, Canad. J. Math. 32 (1980), 893-907. MR 590654
12.
P. D. T. A. Elliott, Multiplicative functions and Ramanujan's τ-function, J. Austral. Math. Soc. Ser. A 30 (1981), 461-468. MR 621561
13.
P. D. T. A. Elliott, Arithmetic functions and integer products, Grundlehren Math. Wiss., vol. 272, Springer-Verlag, Berlin, New York, Tokyo, 1984/1985. MR 766558
14.
P. D. T. A. Elliott, Functional analysis and additive arithmetic functions, Bull. Amer. Math. Soc. (N. S. ) 16 (1987), 179-223. MR 876958
15.
P. D. T. A. Elliott, The norms of compositions of arithmetic operators, Bull. London Math. Soc. (to appear). MR 915428
16.
P. D. T. A. Elliott, C. Moreno and F. Shahidi, On the absolute value of Ramanujan's τ-function, Math. Ann. 266 (1984), 507-511. MR 735531
17.
W. J. Ellison and M. Mendès-France, Les nombres premiers, Hermann, Paris, 1975. MR 417077
18.
G. Halász, Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hungar. 19 (1968), 365-403. MR 230694
19.
G. H. Hardy, Ramanujan. Twelve lectures on subjects suggested by his life and work, Cambridge, 1940. MR 4860
20.
A. Ivić, The theory of the Riemann zeta-function with applications, John Wiley and Sons, Ltd., New York, London, Sydney, Toronto, 1985. MR 792089
21.
J. Kubilius, Probabilistic methods in the theory of numbers, Trans. Math. Monographs, vol. 11, Amer. Math. Soc. Providence, R. I., 1964. MR 160745
22.
E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, 2 Bde., Teubner, Leipzig, 1909.
23.
C. Moreno and F. Shahidi, The fourth moment of Ramanujan τ-function, Math. Ann. 266 (1983), 233-239. MR 724740
24.
J. Opolka and W. Scharlau, From Fermat to Minkowski, Springer-Verlag, Berlin, New York, Tokyo, 1985. MR 770936
25.
K. Prachar, Primzahlverteilung, Grundlehren Math. Wiss., 91, Springer-Verlag, Berlin, 1957. MR 87685
26.
R. Rankin, Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions, Math. Proc. Cambridge Philos. Soc. 35 (1934), 357-372.
27.
R. Rankin, Sums of powers of cusp form coefficients. II, Math. Ann. 272 (1985), 593-600. MR 807293
28.
W. Schwarz, Remarks on the theorem of Elliott and Daboussi; and applications, Elementary and Analytic Theory of Numbers (H. Iwaniec, ed. ), Banach Center Publications, Inst, of Math. Polish Acad. Sci., Warszawa, 1985, pp. 463-498. MR 840490
29.
W. Schwarz and J. Spilker, Eine Anwendung des Approximationssatzes von Weierstrass-Stone auf Ramanujan-Summen, Arch. Wisk. (3) 19 (1971), 198-209. MR 332704
30.
F. Shahidi, On certain L-functions, Amer. J. Math. 103 (1981), 297-355. MR 610479
31.
E. C. Titchmarsh, The Riemann zeta function, Oxford, 1951; new edition (D. R. Heath-Brown, ed. ), Oxford Univ. Press, 1986.
32.
E. Wirsing, Dos asymptotische Verhalten von Summen über multiplikative Funktionen. II, Acta Math. Acad. Sci. Hungar. 18 (1967), 411-467. MR 223318


Additional Information:

Reviewer(s):
P. D. T. A. Elliott

Review Information:
Journal: Bull. Amer. Math. Soc. 18 (1988), 193-209.
DOI: 10.1090/S0273-0979-1988-15648-0
PII: S 0273-0979(1988)15648-0


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google