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Book Review

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Book Information

Author(s): Melvyn B. Nathanson
Title: Elementary methods in number theory
Additional book information: Springer, New York, 2000, xiii + 513, $49.95, 0-38798912-9

References:

[BDD]
R. Balasubramanian, J.-M. Deshouillers and F. Dress, Problème de Waring pour les bicarrés 1, 2, C.R. Acad. Sci. Paris Sér. I Math., 303 (1986) 85-88, and 161-163. MR 87m:11099; MR 88e:11095
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H. Bohr, Address of Professor Harald Bohr, in Proceedings of the International Congress of Mathematicians, Cambridge, 1950, Volume 1, pp. 127-134, Providence, 1952, American Math. Society. MR 13:550c
[Ch]
K. Chandrasekharan, Obituary: S.S. Pillai, Journal of the Indian Math. Society, 15 (1951) 1-10. MR 13:198d
[C]
J.-R. Chen, Waring's problem for $g(5)=37$, Scientia Sinica, 13 (1964) 335 and 1547-68. MR 34:135
[Da]
H. Daboussi, Sur le théorème des nombres premiers, C. R. Acad. Sci. Paris Sér. 1 Math., 298 (1984), no. 8, 161-164. MR 85f:11065
[D]
L.E. Dickson, The Waring problem and its generalizations, Bulletin of the Amer. Math. Soc., 42 (1936) 833-842.
[HR]
G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatory analysis, Proc. London Math. Soc., 17 (1918) 75-115.
[E1]
P. Erdös, On an elementary proof of some asymptotic formulas in the theory of partitions, Annals of Math., 43 (1942) 437-450.MR 4:36a
[E2]
P. Erdös, On a new method in elementary number theory which leads to an elementary proof of the prime number theorem, Proc. Nat. Acad. Sci. U.S.A., 35 (1949) 374-384. MR 10:595c
[H]
D. Hilbert, Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl $n^{ter}$ Potenzen (Waringsches Problem), Math. Annalen, 67 (1909) 281-300.
[Hi]
A. Hildebrand, The prime number theorem via the large sieve, Mathematika, 33 (1986), no. 1, 23-30. MR 88a:11085
[I]
A. Ingham, Review of the papers of Selberg and Erdös, Math. Reviews, 10 (1949) 595b, 595c.
[M]
K. Mahler, On the fractional parts of the powers of a rational number (II), Mathematika, 4 (1957) 122-124. MR 20:33
[P1]
S. Pillai, On Waring's Problem, Journal of Indian Math. Soc.,2 (1936) 16-44.
[P2]
S. Pillai, On Waring's Problem $g(6)=73$, Proc. Indian Acad. Sci., 12A (1940) 30-40. MR 2:146c
[Se]
A. Selberg, An elementary proof of the prime number theorem, Annals of Math., 50 (1949) 305-313. MR 10:595b
[S]
J. Silverman, Wieferich's criterion and the abc conjecture, Journal of Number Theory, 30 (1988), 226-237. MR 89m:11027
[UH]
J.V. Uspensky and M.A. Heaslet, Elementary Number Theory, McGraw Hill Book Company, 1939.MR 1:38d

Additional Information:

Reviewer(s):
M. Ram Murty
Affiliation: Queen's University
Email: murty@mast.queensu.ca

Review Information:
Journal: Bull. Amer. Math. Soc. 38 (2001), 117-121.

MSC (2000): Primary 11-01, 11Axx, 11B13, 11Pxx
DOI: 10.1090/S0273-0979-00-00890-9
PII: S 0273-0979(00)00890-9
Posted: October 2, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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