An additive problem with primes and almost-primes

• Autorzy: T. P. Peneva , D. I. Tolev
• Języki publikacji: EN

Kategorie tematyczne

• 11N36: Applications of sieve methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 83
• Numer: 2
• Strony: 155-169

Daty

wydano

1998

otrzymano

1997-03-24

Twórcy

autor

T. P. Peneva

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

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] Davenport H., Multiplicative Number Theory (revised by H. Montgomery), 2nd ed., Springer, 1980.
• [3] Halberstam H., Richert H.-E., Sieve Methods, Academic Press, London, 1974.
• [4] Hardy G. H., Wright E. M., An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979.
• [5] Heath-Brown D. R., Three primes and an almost-prime in arithmetic progression, J. London Math. Soc. (2) 23 (1981), 396-414.
• [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.
• [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.
• [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).