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]**

*The general sieve*, Acta Arith.

**X**(1964), 31-62. MR

**0167467**

**[BF1]**

*Lagrange's Four Squares Theorem with almost prime variables*, J. Reine Angew. Math.

**454**(1994), 59-96. MR

**1288679**

**[BF2]**

*Le crible à vecteurs*, Compositio math.

**102**(1996), 337-355. MR

**1401427**

**[DHR]**

*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

**1399343**

**[FH]**

*The Brun-Hooley Sieve*, J. Number Theory

**81**(2000), 335-350. MR

**1752258**

**[FI]**

*The polynomial*

*captures its primes*, Annals of Math.

**148**(1998), 945-1040. MR

**1670065**

**[FK]**

*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

**1689544**

**[H-B1]**

*Almost-prime*

*-tuples*, Mathematika

**44**(1997), 245-266. MR

**1600529**

**[H-B2]**

*Primes represented by*, Acta Math.

**186**(2001), 1-84.

**[HR]**

*Sieve Methods*, Academic Press, New York/London, 1974. MR

**0424730**

**[H1]**

*An almost-pure sieve*, Acta Arith.

**LXVI**(1994), 359-368. MR

**1288352**

**[H2]**

*On the intervals between numbers that are sums of two squares: IV*, J. Reine Angew. Math.

**452**(1994), 79-109. MR

**1282197**

**[I]**

*Almost-primes represented by quadratic polynomials*, Invent. Math.

**47**(1978), 171-188. MR

**0485740**

**[JR]**

*An improvement of Selberg's sieve method*, Acta Arith.

**XI**(1965), 217-240. MR

**0202680**

**[Ri]**

*Recent results about Fermat's Last Theorem*, Expositiones Math.

**5**(1987), 75-96. MR

**0880258**

**[R]**

*Selberg's sieve with weights*, Mathematica

**16**(1969), 1-22. MR

**0246850**

**[S]**

*Collected Papers*, vol. II, Springer Verlag, 1991. MR

**1295844**

Review Information:

Reviewer: Heini Halberstam

Affiliation: University of Illinois

Email: heini@math.uiuc.edu

Journal: Bull. Amer. Math. Soc.

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

Published electronically: October 17, 2002

Review copyright: © Copyright 2002 American Mathematical Society