Integers with no large prime factors

• Autorzy: Ti Zuo Xuan
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 69
• Numer: 4
• Strony: 303-327

Daty

wydano

1995

otrzymano

1991-07-02

poprawiono

1993-11-30

Twórcy

autor

Ti Zuo Xuan

• Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China

Bibliografia

• [1] N. G. de Bruijn, On the number of positive integers ≤x and free of prime factors >y, Nederl. Akad. Wetensch. Proc. Ser. A 54 (1951), 50-60.
• [2] N. G. de Bruijn, The asymptotic behavior of a function occurring in the theory of primes, J. Indian Math. Soc. (N.S.) 15 (1951), 25-32.
• [3] H. G. Diamond and H. Halberstam, The combinatorial sieve, in: Number Theory, Proc. 4th Matsci. Conf. Ootacamund/India 1984, Lecture Notes in Math. 1122, Springer, 1985, 63-73
• [4] E. Fouvry et G. Tenenbaum, Entiers sans grand facteur premier en progressions arithmétiques, Proc. London Math. Soc. (3) 63 (1991), 449-494.
• [5] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London, 1974.
• [6] D. G. Hazlewood, Sums over positive integers with few prime factors, J. Number Theory 7 (1975), 189-207.
• [7] A. Hildebrand, On the number of positive integers ≤x and free of prime factors >y, J. Number Theory 22 (1986), 289-307.
• [8] A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290.
• [9] K. K. Norton, Numbers with small prime factors and the least k-th power non residue, Mem. Amer. Math. Soc. 106 (1971).
• [10] H. E. Richert, Zur Abschätzung der Riemannschen Zetafunktion in der Nähe der Vertikalen σ = 1, Math. Ann. 169 (1967), 97-101.
• [11] E. Saias, Sur le nombre des entiers sans grand facteur premier, J. Number Theory 32 (1989), 78-99.
• [12] G. Tenenbaum, Cribler les entiers sans grand facteur premier, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 377-384.
• [13] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed. revised by D. R. Heath-Brown, Oxford, 1986.
• [14] A. I. Vinogradov, On numbers with small prime divisors, Dokl. Akad. Nauk SSSR (N.S.) 109 (1956), 683-686 (in Russian).