ArticleOriginal scientific text

Title

Arithmetic progressions of prime-almost-prime twins

Authors 1

Affiliations

  1. Department of Mathematics, Plovdiv University "P. Hilendarski", "Tsar Asen" 24, Plovdiv 4000, Bulgaria

Bibliography

  1. Brüdern J., Fouvry E., Lagrange's Four Squares Theorem with almost prime variables, J. Reine Angew. Math. 454 (1994), 59-96.
  2. Chen J., On the representation of a large even integer as the sum of a prime and the product of at most two primes, Sci. Sinica 16 (1973), 157-176.
  3. Davenport H., Multiplicative Number Theory (revised by H. Montgomery), 2nd ed., Springer, 1980.
  4. Halberstam H., Richert H.-E., Sieve Methods, Academic Press, London, 1974.
  5. Hardy G. H., Wright E. M., An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979.
  6. Heath-Brown D. R., Three primes and an almost-prime in arithmetic progression, J. London Math. Soc. (2) 23 (1981), 396-414.
  7. Heath-Brown D. R., Prime numbers in short intervals and a generalized Vaughan identity, Canad. J. Math. 34 (1982), 1365-1377.
  8. Iwaniec H., On sums of two norms from cubic fields, in: Journées de théorie additive des nombres, Université de Bordeaux I, 1977, 71-89.
  9. Iwaniec H., Rosser's sieve, Acta Arith. 36 (1980), 171-202.
  10. Iwaniec H., A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320.
  11. Karatsuba A. A., Principles of the Analytic Number Theory, Nauka, Moscow, 1983 (in Russian).
  12. Maier H., Pomerance C., Unusually large gaps between consecutive primes, Trans. Amer. Math. Soc. 322 (1990), 201-237.
  13. Peneva T. P., Tolev D. I., An additive problem with primes and almost-primes, Acta Arith. 83 (1998), 155-169.
  14. Tolev D. I., On the number of representations of an odd integer as a sum of three primes, one of which belongs to an arithmetic progression, Proc. Steklov. Inst. Math. 218 (1997).
  15. van der Corput J. G., Über Summen von Primzahlen und Primzahlquadraten, Math. Ann. 116 (1939), 1-50.
  16. Vaughan R. C., The Hardy-Littlewood Method, Cambridge Univ. Press, 1981.
  17. Vinogradov I. M., Representation of an odd number as a sum of three primes, Dokl. Akad. Nauk SSSR 15 (1937), 169-172 (in Russian).
Pages:
67-98
Main language of publication
English
Received
1998-03-11
Accepted
1998-07-01
Published
1999
Exact and natural sciences