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 0167467
[BF1] J. Brüdern and E. Fouvry, 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] 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 1399343
[FH] K. Ford and H. Halberstam, The Brun-Hooley Sieve, J. Number Theory 81 (2000), 335-350. MR 1752258
[FI] J. Friedlander and H. Iwaniec, The polynomial captures its primes, Annals of Math. 148 (1998), 945-1040. MR 1670065
[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 1689544
[H-B1] D. R. Heath-Brown, Almost-prime -tuples, Mathematika 44 (1997), 245-266. MR 1600529
[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 0424730
[H1] C. Hooley, 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] H. Iwaniec, Almost-primes represented by quadratic polynomials, Invent. Math. 47 (1978), 171-188. MR 0485740
[JR] W. B. Jurkat and H.-E. Richert, An improvement of Selberg's sieve method, Acta Arith. XI (1965), 217-240. MR 0202680
[Ri] P. Ribenboim, Recent results about Fermat's Last Theorem, Expositiones Math. 5 (1987), 75-96. MR 0880258
[R] H.-E. Richert, Selberg's sieve with weights, Mathematica 16 (1969), 1-22. MR 0246850
[S] A. Selberg, Collected Papers, vol. II, Springer Verlag, 1991. MR 1295844
- [AO]
- N. C. Ankeny and H. Onishi, The general sieve, Acta Arith. X (1964), 31-62. MR 0167467
- [BF1]
- J. Brüdern and E. Fouvry, 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]
- 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 1399343
- [FH]
- K. Ford and H. Halberstam, The Brun-Hooley Sieve, J. Number Theory 81 (2000), 335-350. MR 1752258
- [FI]
- J. Friedlander and H. Iwaniec, The polynomial captures its primes, Annals of Math. 148 (1998), 945-1040. MR 1670065
- [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 1689544
- [H-B1]
- D. R. Heath-Brown, Almost-prime -tuples, Mathematika 44 (1997), 245-266. MR 1600529
- [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 0424730
- [H1]
- C. Hooley, 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]
- H. Iwaniec, Almost-primes represented by quadratic polynomials, Invent. Math. 47 (1978), 171-188. MR 0485740
- [JR]
- W. B. Jurkat and H.-E. Richert, An improvement of Selberg's sieve method, Acta Arith. XI (1965), 217-240. MR 0202680
- [Ri]
- P. Ribenboim, Recent results about Fermat's Last Theorem, Expositiones Math. 5 (1987), 75-96. MR 0880258
- [R]
- H.-E. Richert, Selberg's sieve with weights, Mathematica 16 (1969), 1-22. MR 0246850
- [S]
- A. Selberg, 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