Book Review
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Book Information:
Author:
Melvyn B. Nathanson
Title:
Elementary methods in number theory
Additional book information:
Springer,
New York,
2000,
xiii + 513 pp.,
ISBN 0-38798912-9,
$49.95$
[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 0853592; MR 88e:11095
[B] 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 
, Scientia Sinica, 13 (1964) 335 and 1547-68. MR 0200236
[Da] H. Daboussi, Sur le théorème des nombres premiers, C. R. Acad. Sci. Paris Sér. 1 Math., 298 (1984), no. 8, 161-164. MR 0741085
[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 
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 0859495
[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 0093509
[P1] S. Pillai, On Waring's Problem, Journal of Indian Math. Soc.,2 (1936) 16-44.
[P2] S. Pillai, On Waring's Problem 
, 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 0961918
[UH] J.V. Uspensky and M.A. Heaslet, Elementary Number Theory, McGraw Hill Book Company, 1939.MR 1:38d
- [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 0853592; MR 88e:11095
- [B]
- 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 , Scientia Sinica, 13 (1964) 335 and 1547-68. MR 0200236
- [Da]
- H. Daboussi, Sur le théorème des nombres premiers, C. R. Acad. Sci. Paris Sér. 1 Math., 298 (1984), no. 8, 161-164. MR 0741085
- [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 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 0859495
- [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 0093509
- [P1]
- S. Pillai, On Waring's Problem, Journal of Indian Math. Soc.,2 (1936) 16-44.
- [P2]
- S. Pillai, On Waring's Problem , 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 0961918
- [UH]
- J.V. Uspensky and M.A. Heaslet, Elementary Number Theory, McGraw Hill Book Company, 1939.MR 1:38d
Review Information:
Reviewer:
M. Ram Murty
Affiliation:
Queen’s University
Email:
murty@mast.queensu.ca
Journal:
Bull. Amer. Math. Soc.
38 (2001), 117-121
Published electronically:
October 2, 2000
Review copyright:
© Copyright 2000
American Mathematical Society
