Book Review

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Book Information:

Author: George Greaves

Title: Sieves in number theory

Additional book information: Springer-Verlag, New York, 2001, xii+304 pp., ISBN 3-540-41647-1, 94.95 euros

**[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**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**and*, 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**-tuples*, Mathematika**44**(1997), 245-266. MR**99a:11106****[H-B2]**-,*Primes represented by*, 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**

Review Information:

Reviewer: Heini Halberstam

Affiliation: University of Illinois

Email: heini@math.uiuc.edu

Journal: Bull. Amer. Math. Soc.

**40**(2003), 109-119

MSC (2000): Primary 11N35, 11N36

Published electronically: October 17, 2002

Review copyright: © Copyright 2002 American Mathematical Society