Arithmetic progressions of prime-almost-prime twins
D. I. Tolev
Acta Arithmetica, Tome 89 (1999), p. 67-98 / Harvested from The Polish Digital Mathematics Library
Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:207232
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     author = {D. I. Tolev},
     title = {Arithmetic progressions of prime-almost-prime twins},
     journal = {Acta Arithmetica},
     volume = {89},
     year = {1999},
     pages = {67-98},
     zbl = {0929.11043},
     language = {en},
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D. I. Tolev. Arithmetic progressions of prime-almost-prime twins. Acta Arithmetica, Tome 89 (1999) pp. 67-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav88i1p67bwm/

[000] [1] Brüdern J., Fouvry E., Lagrange's Four Squares Theorem with almost prime variables, J. Reine Angew. Math. 454 (1994), 59-96. | Zbl 0809.11060

[001] [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. | Zbl 0319.10056

[002] [3] Davenport H., Multiplicative Number Theory (revised by H. Montgomery), 2nd ed., Springer, 1980. | Zbl 0453.10002

[003] [4] Halberstam H., Richert H.-E., Sieve Methods, Academic Press, London, 1974. | Zbl 0298.10026

[004] [5] Hardy G. H., Wright E. M., An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979. | Zbl 0423.10001

[005] [6] Heath-Brown D. R., Three primes and an almost-prime in arithmetic progression, J. London Math. Soc. (2) 23 (1981), 396-414. | Zbl 0425.10051

[006] [7] Heath-Brown D. R., Prime numbers in short intervals and a generalized Vaughan identity, Canad. J. Math. 34 (1982), 1365-1377. | Zbl 0478.10024

[007] [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.

[008] [9] Iwaniec H., Rosser's sieve, Acta Arith. 36 (1980), 171-202. | Zbl 0435.10029

[009] [10] Iwaniec H., A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. | Zbl 0444.10038

[010] [11] Karatsuba A. A., Principles of the Analytic Number Theory, Nauka, Moscow, 1983 (in Russian).

[011] [12] Maier H., Pomerance C., Unusually large gaps between consecutive primes, Trans. Amer. Math. Soc. 322 (1990), 201-237. | Zbl 0706.11052

[012] [13] Peneva T. P., Tolev D. I., An additive problem with primes and almost-primes, Acta Arith. 83 (1998), 155-169. | Zbl 0898.11037

[013] [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). | Zbl 0911.11048

[014] [15] van der Corput J. G., Über Summen von Primzahlen und Primzahlquadraten, Math. Ann. 116 (1939), 1-50.

[015] [16] Vaughan R. C., The Hardy-Littlewood Method, Cambridge Univ. Press, 1981. | Zbl 0455.10034

[016] [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).