Bulletin of the American Mathematical Society

MathSciNet review: 1567833
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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.

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

[DDT] J.-M. Deshouillers, F. Dress, and G. Tenenbaum, Loi de répartition des diviseurs. I, Acta Arith. 34 (1979), 273-285. MR 0543201




[EK] 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




[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.




[Er] P. Erdös, On the distribution function of additive functions, Ann. of Math. (2) 47 (1946), 1-20. MR 15424




[Ho] C. Hooley, On a new technique and its applications to the theory of numbers, Proc. London Math. Soc. (3) 38 (1979), 115-151. MR 520975




[HR] G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Quart. J. Math. 48 (1917), 76-92.




[HT1] R. R. Hall and G. Tenenbaum, Sur la proximité des diviseurs, Recent Progress in Analytic Number Theory (H. Halberstam and C. Hooley, eds.), Academic Press, London 1981, vol. 1, pp. 103-113. MR 637344




[HT2] R. R. Hall and G. Tenenbaum, The average orders of Hooley's Δ_r-functions, Compositio Math. 60 (1986), 163-186. MR 868136




[Ma] H. Maier, On the Moebius function, Trans. Amer. Math. Soc. 301 (1987), 649-664. MR 882708




[MT1] H. Maier and G. Tenenbaum, On the set of divisors of an integer, Invent. Math. 76 (1984), 121-128. MR 739628




[MT2] H. Maier and G. Tenenbaum, On the normal concentration of divisors, J. London Math. Soc. (2) 31 (1985), 393-400. MR 812767




[Tel] G. Tenenbaum, Loi de répartition des diviseurs. II, Acta Arith. 38 (1980), 1-36. MR 574122




[Te2] G. Tenenbaum, Sur la concentration moyenne des diviseurs, Comment. Math. Helv. 60 (1985), 411-428. MR 814148




[Va] R. C. Vaughan, On Waring's problem for smaller exponents II, Mathematika 33 (1986), 6-22. MR 859494