Book Review
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MathSciNet review:
1566911
Full text of review:
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Book Information:
Authors:
H. H. Halberstam and
H.-E. Richert
Title:
Sieve methods
Additional book information:
Academic Press, London, 1974, xiii + 364 pp., $26.00.
Enrico Bombieri, Le grand crible dans la théorie analytique des nombres, Astérisque, No. 18, Société Mathématique de France, Paris, 1974 (French). Avec une sommaire en anglais. MR 0371840
Enrico Bombieri, On twin almost primes, Acta Arith. 28 (1975/76), no. 2, 177–193. MR 396435, DOI 10.4064/aa-28-2-177-193
Enrico Bombieri, The asymptotic sieve, Rend. Accad. Naz. XL (5) 1(2) (1975/76), 243–269 (1977) (English, with Italian summary). MR 491570
Jing Run Chen, On the representation of a larger even integer as the sum of a prime and the product of at most two primes, Sci. Sinica 16 (1973), 157–176. MR 434997
P. X. Gallagher, A larger sieve, Acta Arith. 18 (1971), 77–81. MR 291120, DOI 10.4064/aa-18-1-77-81
H. Halberstam and K. F. Roth, Sequences. Vol. I, Clarendon Press, Oxford, 1966. MR 0210679
C. Hooley, Applications of sieve methods to the theory of numbers, Cambridge Tracts in Mathematics, No. 70, Cambridge University Press, Cambridge-New York-Melbourne, 1976. MR 0404173
H. Iwaniec, On the error term in the linear sieve, Acta Arith. 19 (1971), 1–30. MR 296043, DOI 10.4064/aa-19-1-1-30
H. Iwaniec, The half dimensional sieve, Acta Arith. 29 (1976), no. 1, 69–95. MR 412134, DOI 10.4064/aa-29-1-69-95
H. L. Montgomery and R. C. Vaughan, The large sieve, Mathematika 20 (1973), 119–134. MR 374060, DOI 10.1112/S0025579300004708
11. J. W. Porter, An improvement of the upper and lower bound functions of Ankeny and Onishi, Acta Arith. (to appear).
P. M. Ross, On Chen’s theorem that each large even number has the form $p_{1}+p_{2}$ or $p_{1}+p_{2}p_{3}$, J. London Math. Soc. (2) 10 (1975), no. 4, 500–506. MR 389816, DOI 10.1112/jlms/s2-10.4.500
Atle Selberg, Sieve methods, 1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969) Amer. Math. Soc., Providence, R.I., 1971, pp. 311–351. MR 0567686
Atle Selberg, Remarks on sieves, Proceedings of the Number Theory Conference (Univ. Colorado, Boulder, Colo., 1972) Univ. Colorado, Boulder, Colo., 1972, pp. 205–216. MR 0389802
R. C. Vaughan, Mean value theorems in prime number theory, J. London Math Soc. (2) 10 (1975), 153–162. MR 0376567, DOI 10.1112/jlms/s2-10.2.153
- 1.
- E. Bombieri, Le grand crible dans la théorie analytique des nombres, Astérisque No. 18, Société Mathématique de France, Paris, 1974. MR 51 #8057. MR 0371840
- 2.
- E. Bombieri, On twin almost primes, Acta Arith. 28 (1975), 177-193; corrigendum, ibid., 28 (1976), 760-763. MR 396435
- 3.
- E. Bombieri, The asymptotic sieve (to appear). MR 491570
- 4.
- J. Chen, On the representation of a large even integer as the sum of a prime and a product of two primes, Sci. Sinica 16 (1973), 157-176. MR 434997
- 5.
- P. X. Gallagher, A larger sieve, Acta Arith. 18 (1971), 77-81. MR 45 #214. MR 291120
- 6.
- H. Halberstam and K. F. Roth, Sequences. I, Clarendon Press, Oxford, 1966. MR 35 #1565. MR 210679
- 7.
- C. Hooley, Applications of sieve methods to the theory of numbers, Cambridge Tracts in Math., no. 70, Cambridge Univ. Press, London and New York, 1976. MR 404173
- 8.
- H. Iwaniec, On the error term in the linear sieve, Acta Arith. 19 (1971), 1-30. MR 45 #5104. MR 296043
- 9.
- H. Iwaniec, The half dimensional sieve, Acta Arith. 29 (1976), 69-95. MR 412134
- 10.
- H. L. Montgomery and R. C. Vaughan, The large sieve, Mathematika 20 (1973), 119-134. MR 374060
- 11.
- J. W. Porter, An improvement of the upper and lower bound functions of Ankeny and Onishi, Acta Arith. (to appear).
- 12.
- P. M. Ross, On Chen's theorem that each large even number has the form p1 + p2 or P1 + P2P3, J. London Math. Soc. (2) 10 (1975), 500-506. MR 389816
- 13.
- A. Selberg, Sieve methods, Proc. Sympos. Pure Math., vol 20, Amer. Math. Soc., Providence, R. I., 1971, pp. 311-351. MR 47 #3286. MR 567686
- 14.
- A. Selberg, Remarks on sieves, Proc. Number Theory Conf. (Boulder, Colo., 1972), Univ. of Colorado, 1972, pp. 205-216. MR 50 #4457. MR 389802
- 15.
- R. C. Vaughan, Mean value theorems in prime number theory, J. London Math. Soc. (2) 10 (1975), 153-162. MR 376567
Review Information:
Reviewer:
H. L. Montgomery
Journal:
Bull. Amer. Math. Soc.
82 (1976), 846-853
DOI:
https://doi.org/10.1090/S0002-9904-1976-14180-8
