Numbers with a large prime factor

• Autorzy: R. C. Baker , G. Harman
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 73
• Numer: 2
• Strony: 119-145

Daty

wydano

1995

otrzymano

1994-08-01

poprawiono

1995-02-21

Twórcy

autor

R. C. Baker

• Department of Mathematics, Brigham Young University, Provo, Utah 84602, U.S.A.

autor

G. Harman

• Mathematics Institute, University of Wales, Senghennydd Road, Cardiff CF2 4AG, U.K.

Bibliografia

• [1] R. C. Baker, The greatest prime factor of the integers in an interval, Acta Arith. 47 (1986), 193-231.
• [2] R. C. Baker, G. Harman and J. Rivat, Primes of the form $[n^c]$, J. Number Theory, to appear.
• [3] E. Bombieri and H. Iwaniec, On the order of ζ(1/2 + it), Ann. Scuola Norm. Sup. Pisa 13 (1986), 449-472.
• [4] A. Y. Cheer and D. A. Goldston, A differential delay equation arising from the sieve of Eratosthenes, Math. Comp. 55 (1990), 129-141.
• [5] H. Davenport, Multiplicative Number Theory, 2nd ed. revised by H. L. Montgomery, Springer, New York, 1980.
• [6] E. Fouvry, Sur le théorème de Brun-Titchmarsh, Acta Arith. 43 (1984), 417-424.
• [7] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333.
• [8] J. B. Friedlander, Integers free from large and small primes, Proc. London Math. Soc. 33 (1986), 565-576.
• [9] S. W. Graham, The greatest prime factor of the integers in an interval, J. London Math. Soc. 24 (1981), 427-440.
• [10] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, 1991.
• [11] G. Harman, On the distribution of αp modulo one, J. London Math. Soc. 27 (2) (1983), 9-13.
• [12] C. H. Jia, The greatest prime factor of integers in short intervals II, Acta Math. Sinica 32 (1989), 188-199 (in Chinese).
• [13] H.-Q. Liu, The greatest prime factor of the integers in an interval, Acta Arith. 65 (1993), 301-328.
• [14] S. H. Min, Methods in Number Theory, Vol. 2, Science Press, 1983 (in Chinese).
• [15] K. Ramachandra, A note on numbers with a large prime factor, J. London Math. Soc. 1 (2) (1969), 303-306.
• [16] K. Ramachandra, A note on numbers with a large prime factor, II, J. Indian Math. Soc. 34 (1970), 39-48.
• [17] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, revised by D. R. Heath-Brown, Oxford University Press, 1986.
• [18] I. M. Vinogradov, The Method of Trigonometrical Sums in the Theory of Numbers, translated and annotated by A. Davenport and K. F. Roth, Wiley, New York, 1954.
• [19] N. Watt, Exponential sums and the Riemann zeta function II, J. London Math. Soc. 39 (1989), 385-404.
• [20] J. Wu, P₂ dans les petits intervalles, in: Séminaire de Théorie des Nombres, Paris 1989-90, Birkhäuser, 1992, 233-267