# An additive problem with primes and almost-primes

Acta Arithmetica (1998)

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

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topT. P. Peneva, and D. I. Tolev. "An additive problem with primes and almost-primes." Acta Arithmetica 83.2 (1998): 155-169. <http://eudml.org/doc/207112>.

@article{T1998,

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 = {http://eudml.org/doc/207112},

volume = {83},

year = {1998},

}

TY - JOUR

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 - http://eudml.org/doc/207112

ER -

## References

top- [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] Davenport H., Multiplicative Number Theory (revised by H. Montgomery), 2nd ed., Springer, 1980. Zbl0453.10002
- [3] Halberstam H., Richert H.-E., Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
- [4] Hardy G. H., Wright E. M., An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979. Zbl0423.10001
- [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] Karatsuba A. A., Principles of Analytic Number Theory, Nauka, Moscow, 1983 (in Russian).
- [7] Maier H., Pomerance C., Unusually large gaps between consecutive primes, Trans. Amer. Math. Soc. 322 (1990), 201-237. Zbl0706.11052
- [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] van der Corput J. G., Über Summen von Primzahlen und Primzahlquadraten, Math. Ann. 116 (1939), 1-50.
- [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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