Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 1567833
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Richard R. Hall and Gérald Tenenbaum
Title: Divisors
Additional book information: Cambridge Tracts in Mathematics, Vol. 90. Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, and Sydney, 1988, xvi + 167 pp., $39.50. ISBN 0-521-34056-x.

References [Enhancements On Off] (What's this?)

  • Jean-Marc Deshouillers, François Dress, and Gérald Tenenbaum, Lois de répartition des diviseurs. I, Acta Arith. 34 (1979), no. 4, 273–285 (loose errata) (French). MR 543201, DOI 10.4064/aa-34-4-273-285
  • P. Erdös and M. Kac, The Gaussian law of errors in the theory of additive number theoretic functions, Amer. J. Math. 62 (1940), 738–742. MR 2374, DOI 10.2307/2371483
    • [E1] P. D. T. A. Elliott, Review of "Intégration et théorie des nombres" by Jean-Loup Mauclaire, Bull. Amer. Math. Soc. (N. S.) 18 (1988), 193-209.

  • P. Erdös, On the distribution function of additive functions, Ann. of Math. (2) 47 (1946), 1–20. MR 15424, DOI 10.2307/1969031
  • C. Hooley, On a new technique and its applications to the theory of numbers, Proc. London Math. Soc. (3) 38 (1979), no. 1, 115–151. MR 520975, DOI 10.1112/plms/s3-38.1.115
    • [HR] G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Quart. J. Math. 48 (1917), 76-92.

  • R. R. Hall and G. Tenenbaum, Sur la proximité des diviseurs, Recent progress in analytic number theory, Vol. 1 (Durham, 1979) Academic Press, London-New York, 1981, pp. 103–113 (French). MR 637344
  • R. R. Hall and G. Tenenbaum, The average orders of Hooley’s $\Delta _r$-functions. II, Compositio Math. 60 (1986), no. 2, 163–186. MR 868136
  • Helmut Maier, On the Möbius function, Trans. Amer. Math. Soc. 301 (1987), no. 2, 649–664. MR 882708, DOI 10.1090/S0002-9947-1987-0882708-5
  • H. Maier and G. Tenenbaum, On the set of divisors of an integer, Invent. Math. 76 (1984), no. 1, 121–128. MR 739628, DOI 10.1007/BF01388495
  • H. Maier and G. Tenenbaum, On the normal concentration of divisors, J. London Math. Soc. (2) 31 (1985), no. 3, 393–400. MR 812767, DOI 10.1112/jlms/s2-31.3.393
  • Gérald Tenenbaum, Lois de répartition des diviseurs. II, Acta Arith. 38 (1980/81), no. 1, 1–36 (French). MR 574122, DOI 10.4064/aa-38-1-1-36
  • Gérald Tenenbaum, Sur la concentration moyenne des diviseurs, Comment. Math. Helv. 60 (1985), no. 3, 411–428 (French). MR 814148, DOI 10.1007/BF02567424
  • R. C. Vaughan, On Waring’s problem for smaller exponents. II, Mathematika 33 (1986), no. 1, 6–22. MR 859494, DOI 10.1112/S0025579300013838
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    Review Information:

    Reviewer: Adolf Hildebrand
    Journal: Bull. Amer. Math. Soc. 22 (1990), 159-165
    DOI: https://doi.org/10.1090/S0273-0979-1990-15871-9