Arithmetic progressions of prime-almost-prime twins

• Autorzy: D. I. Tolev
• Języki publikacji: EN

Kategorie tematyczne

• 11N36: Applications of sieve methods
• 11P32: Goldbach-type theorems; other additive questions involving primes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 88
• Numer: 1
• Strony: 67-98

Daty

wydano

1999

otrzymano

1998-03-11

poprawiono

1998-07-01

Twórcy

autor

D. I. Tolev

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

Bibliografia

• [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).