An additive problem with primes and almost-primes

T. P. Peneva; D. I. Tolev

Acta Arithmetica (1998)

  • Volume: 83, Issue: 2, page 155-169
  • ISSN: 0065-1036

How to cite


T. P. Peneva, and D. I. Tolev. "An additive problem with primes and almost-primes." Acta Arithmetica 83.2 (1998): 155-169. <>.

author = {T. P. Peneva, D. I. Tolev},
journal = {Acta Arithmetica},
keywords = {primes; almost-primes; circle method; Bombieri-Vinogradov type results},
language = {eng},
number = {2},
pages = {155-169},
title = {An additive problem with primes and almost-primes},
url = {},
volume = {83},
year = {1998},

AU - T. P. Peneva
AU - D. I. Tolev
TI - An additive problem with primes and almost-primes
JO - Acta Arithmetica
PY - 1998
VL - 83
IS - 2
SP - 155
EP - 169
LA - eng
KW - primes; almost-primes; circle method; Bombieri-Vinogradov type results
UR -
ER -


  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] Davenport H., Multiplicative Number Theory (revised by H. Montgomery), 2nd ed., Springer, 1980. Zbl0453.10002
  3. [3] Halberstam H., Richert H.-E., Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
  4. [4] Hardy G. H., Wright E. M., An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979. Zbl0423.10001
  5. [5] Heath-Brown D. R., Three primes and an almost-prime in arithmetic progression, J. London Math. Soc. (2) 23 (1981), 396-414. Zbl0425.10051
  6. [6] Karatsuba A. A., Principles of Analytic Number Theory, Nauka, Moscow, 1983 (in Russian). 
  7. [7] Maier H., Pomerance C., Unusually large gaps between consecutive primes, Trans. Amer. Math. Soc. 322 (1990), 201-237. Zbl0706.11052
  8. [8] 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 Math. Inst., to appear. Zbl0911.11048
  9. [9] van der Corput J. G., Über Summen von Primzahlen und Primzahlquadraten, Math. Ann. 116 (1939), 1-50. 
  10. [10] Vinogradov I. M., Representation of an odd number as a sum of three primes, Dokl. Akad. Nauk SSSR 15 (1937), 169-172 (in Russian). 

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