Arithmetic progressions of prime-almost-prime twins

D. I. Tolev

Acta Arithmetica (1999)

  • Volume: 88, Issue: 1, page 67-98
  • ISSN: 0065-1036

How to cite

top

D. I. Tolev. "Arithmetic progressions of prime-almost-prime twins." Acta Arithmetica 88.1 (1999): 67-98. <http://eudml.org/doc/207232>.

@article{D1999,
author = {D. I. Tolev},
journal = {Acta Arithmetica},
keywords = {almost primes; arithmetic progressions; three-term arithmetic progressions of distinct primes; circle method},
language = {eng},
number = {1},
pages = {67-98},
title = {Arithmetic progressions of prime-almost-prime twins},
url = {http://eudml.org/doc/207232},
volume = {88},
year = {1999},
}

TY - JOUR
AU - D. I. Tolev
TI - Arithmetic progressions of prime-almost-prime twins
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 1
SP - 67
EP - 98
LA - eng
KW - almost primes; arithmetic progressions; three-term arithmetic progressions of distinct primes; circle method
UR - http://eudml.org/doc/207232
ER -

References

top
  1. [1] Brüdern J., Fouvry E., Lagrange's Four Squares Theorem with almost prime variables, J. Reine Angew. Math. 454 (1994), 59-96. Zbl0809.11060
  2. [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. Zbl0319.10056
  3. [3] Davenport H., Multiplicative Number Theory (revised by H. Montgomery), 2nd ed., Springer, 1980. Zbl0453.10002
  4. [4] Halberstam H., Richert H.-E., Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
  5. [5] Hardy G. H., Wright E. M., An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979. Zbl0423.10001
  6. [6] Heath-Brown D. R., Three primes and an almost-prime in arithmetic progression, J. London Math. Soc. (2) 23 (1981), 396-414. Zbl0425.10051
  7. [7] Heath-Brown D. R., Prime numbers in short intervals and a generalized Vaughan identity, Canad. J. Math. 34 (1982), 1365-1377. Zbl0478.10024
  8. [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. [9] Iwaniec H., Rosser's sieve, Acta Arith. 36 (1980), 171-202. Zbl0435.10029
  10. [10] Iwaniec H., A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. Zbl0444.10038
  11. [11] Karatsuba A. A., Principles of the Analytic Number Theory, Nauka, Moscow, 1983 (in Russian). 
  12. [12] Maier H., Pomerance C., Unusually large gaps between consecutive primes, Trans. Amer. Math. Soc. 322 (1990), 201-237. Zbl0706.11052
  13. [13] Peneva T. P., Tolev D. I., An additive problem with primes and almost-primes, Acta Arith. 83 (1998), 155-169. Zbl0898.11037
  14. [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). Zbl0911.11048
  15. [15] van der Corput J. G., Über Summen von Primzahlen und Primzahlquadraten, Math. Ann. 116 (1939), 1-50. 
  16. [16] Vaughan R. C., The Hardy-Littlewood Method, Cambridge Univ. Press, 1981. Zbl0455.10034
  17. [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). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.