ArticleOriginal scientific text

Title

Integers without large prime factors in short intervals and arithmetic progressions

Authors 1

Affiliations

  1. School of Mathematics, Cardiff University, P.O.Box No. 926, Cardiff CF2 4YH, Wales, U.K.

Bibliography

  1. R. C. Baker, The greatest prime factor of the integers in an interval, Acta Arith. 47 (1986), 193-231.
  2. R. C. Baker and G. Harman, Shifted primes without large prime factors, ibid. 83 (1998), 331-361.
  3. A. Balog, p+a without large prime factors, Sém. Théorie des Nombres Bordeaux (1983-84), exposé 31.
  4. A. Balog and C. Pomerance, The distribution of smooth numbers in arithmetic progressions, Proc. Amer. Math. Soc. 115 (1992), 33-43.
  5. D. A. Burgess, On character sums and L-series, II, Proc. London Math. Soc. (3) 13 (1963), 525-536.
  6. D. A. Burgess, The character sum estimate with r=3, J. London Math. Soc. (2) 33 (1986), 219-226.
  7. J. B. Friedlander, Integers free from large and small primes, Proc. London Math. Soc. (3) 33 (1976), 565-576.
  8. J. B. Friedlander, Shifted primes without large prime factors, in: Number Theory and Applications, 1989, Kluwer, Berlin, 1990, 393-401.
  9. J. B. Friedlander and A. Granville, Smoothing `smooth' numbers, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 339-347.
  10. J. B. Friedlander and J. C. Lagarias, On the distribution in short intervals of integers having no large prime factor, J. Number Theory 25 (1987), 249-273.
  11. S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, London Math. Soc. Lecture Note Ser. 126, Cambridge Univ. Press, 1991.
  12. A. Granville, Integers, without large prime factors, in arithmetic progressions I, Acta Math. 170 (1993), 255-273.
  13. A. Granville, Integers, without large prime factors, in arithmetic progressions II, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 349-362.
  14. G. Harman, Diophantine approximation with square-free integers, Math. Proc. Cambridge Philos. Soc. 95 (1984), 381-388.
  15. G. Harman, Short intervals containing numbers without large prime factors, ibid. 109 (1991), 1-5.
  16. H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202.
  17. H. W. Lenstra, Jr., J. Pila and C. Pomerance, A hyperelliptic smoothness test I, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 397-408.
  18. H.-Q. Liu and J. Wu, Numbers with a large prime factor, Acta Arith. 89 (1999), 163-187.
  19. H. L. Montgomery, Topics in Multiplicative Number Theory, Springer, 1971.
Pages:
279-289
Main language of publication
English
Received
1999-02-19
Published
1999
Exact and natural sciences