zbMATH — the first resource for mathematics

Almost-primes represented by quadratic polynomials. (English) Zbl 0389.10031

11N35 Sieves
11N13 Primes in congruence classes
11N05 Distribution of primes
Full Text: DOI EuDML
[1] Bateman, P.T., Horn, R.A.: A heuristic asymptotic formula concerning the distribution of prime numbers. Math. Comput.16, 363–367 (1962) · Zbl 0105.03302
[2] Buchstab, A.A.: Combinatorial intensification of the sieve method of Eratosthenes (in Russian). Uspehi Mat. Nauk22, no. 3 (135), 199–226 (1967)
[3] Chen, J.-R.: On the distribution of almost-primes in an interval. Sci. Sinica18, 611–627 (1975) · Zbl 0381.10033
[4] Friedlander, J., Iwaniec, H.: Quadratic polynomials and quadratic forms, (to appear in Acta Math.), · Zbl 0393.10049
[5] Halberstam, H., Richert, H.-E.: Almost-primes in short intervals and arithmetic progressions (unpublished), · Zbl 0461.10041
[6] Hardy, G.H., Littlewood, J.E.: Some problems of Partitio Numerorum III. Acta Math.44, 1–70 (1923) · JFM 48.0143.04
[7] Hooley, C.: On the problem of divisors of quadratic polynomials. Acta Math.,110, 97–114 (1963) · Zbl 0116.03802
[8] Hooley, C.: On the greatest prime factor of a quadratic polynomial. Acta Math.117, 281–299 (1967) · Zbl 0146.05704
[9] Hooley, C.: On the Brun-Titchmarsh theorem. II. Proc. London Math. Soc.3 (30), 114–128 (1975) · Zbl 0301.10040
[10] Hooley, C.: On the Brun-Titchmarsh theorem. J. Reine Angew. Math.255, 60–79 (1972) · Zbl 0252.10045
[11] Iwaniec, H.: A new form of the error term in the linear sieve (to appear in Acta Arith.) · Zbl 0444.10038
[12] Kuhn, P.: Neue Abschätzungen auf Grund der Viggo Brunschen Siebmethode, pp. 160–168, 12. Skand. Math. Kongr., Lund, 1953 · Zbl 0058.27505
[13] Kuhn, P.: Über die Primteiler eines Polynoms. Proc. Internat. Congress Math. Amsterdam,2, 35–37 (1954)
[14] Levin, B.V.: A one-dimensional sieve (in Russian). Acta Arith.10, 387–397 (1964)
[15] Motohashi, Y.: On some improvements of the Brun-Titchmarsh theorem, III. J. Math. Soc. Japan,27, 444–453 (1975) · Zbl 0309.10018
[16] Rademacher, H.: Beiträge zur Viggo Brunschen Methode in der Zahlentheorie. Abh. Math. Sem. Univ. Hamburg3, 12–30 (1924) · JFM 49.0128.05
[17] Ricci, G.: Su la congettura di Goldbach e la costante di Schnirelman. I. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Math. (2),6, 91–116 (1937)
[18] Richert, H.-E.: Selberg’s sieve with weights. Mathematika16, 1–22 (1969) · Zbl 0192.39703
[19] Schinzel, A., Sierpiński, W.: Sur certaines hypothèses concernant les nombres premiers. Acta Arith.4, 185–208 (1958) · Zbl 0082.25802
[20] Smith, H.J.S.: Report on the theory of numbers. Collected mathematical papers. Vol. I, reprinted, Chelsea 1965,
[21] Wang, Y.: On sieve methods and some of their applications (in Chinese). Acta Math. Sinica9, 432–441 (1959) · Zbl 0147.29702
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.