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Book Review

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Book Information

Author(s): George Greaves
Title: Sieves in number theory
Additional book information: Springer-Verlag, New York, 2001, xii+304, 94.95 euros, 3-540-41647-1

References:

[AO]
N. C. Ankeny and H. Onishi, The general sieve, Acta Arith. X (1964), 31-62. MR 29:4740

[BF1]
J. Brüdern and E. Fouvry, Lagrange's Four Squares Theorem with almost prime variables, J. Reine Angew. Math. 454 (1994), 59-96. MR 96e:11125

[BF2]
-, Le crible à vecteurs, Compositio math. 102 (1996), 337-355. MR 97f:11079

[DHR]
H. Diamond, H. Halberstam and H.-E. Richert, Combinatorial Sieves of Dimension exceeding one, II, Analytic Number Theory, Proc. of a Conference in Honor of Heini Halberstam, Birkhäuser, 1996, pp. 265-308. MR 97e:11112

[FH]
K. Ford and H. Halberstam, The Brun-Hooley Sieve, J. Number Theory 81 (2000), 335-350. MR 2001d:11095

[FI]
J. Friedlander and H. Iwaniec, The polynomial $X^{2}+Y^{4}$ captures its primes, Annals of Math. 148 (1998), 945-1040. MR 2000c:11150a

[FK]
K. Ford and S. Konyagin, On two conjectures of Sierpinski concerning the arithmetic functions $\sigma $ and $\phi $, Proceedings of Conference in Honor of A Schinzel, de Gruyter, Berlin (1999), 795-803. MR 2000d:11120

[H-B1]
D. R. Heath-Brown, Almost-prime $k$-tuples, Mathematika 44 (1997), 245-266. MR 99a:11106

[H-B2]
-, Primes represented by $x^{3}+2y^{3}$, Acta Math. 186 (2001), 1-84.

[HR]
H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, New York/London, 1974. MR 54:12689

[H1]
C. Hooley, An almost-pure sieve, Acta Arith. LXVI (1994), 359-368. MR 95g:11092

[H2]
-, On the intervals between numbers that are sums of two squares: IV, J. Reine Angew. Math. 452 (1994), 79-109. MR 95j:11090

[I]
H. Iwaniec, Almost-primes represented by quadratic polynomials, Invent. Math. 47 (1978), 171-188. MR 58:5553

[JR]
W. B. Jurkat and H.-E. Richert, An improvement of Selberg's sieve method, Acta Arith. XI (1965), 217-240. MR 34:2540

[Ri]
P. Ribenboim, Recent results about Fermat's Last Theorem, Expositiones Math. 5 (1987), 75-96. MR 89c:11046

[R]
H.-E. Richert, Selberg's sieve with weights, Mathematica 16 (1969), 1-22. MR 40:119

[S]
A. Selberg, Collected Papers, vol. II, Springer Verlag, 1991. MR 95g:01032

Additional Information:

Reviewer(s):
Heini Halberstam
Affiliation: University of Illinois
Email: heini@math.uiuc.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 40 (2003), 109-119.

MSC (2000): Primary 11N35, 11N36
DOI: 10.1090/S0273-0979-02-00957-6
PII: S 0273-0979(02)00957-6
Posted: October 17, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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