Integers without large prime factors in short intervals and arithmetic progressions

Glyn Harman

Acta Arithmetica (1999)

  • Volume: 91, Issue: 3, page 279-289
  • ISSN: 0065-1036

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Glyn Harman. "Integers without large prime factors in short intervals and arithmetic progressions." Acta Arithmetica 91.3 (1999): 279-289. <http://eudml.org/doc/207356>.

@article{GlynHarman1999,
author = {Glyn Harman},
journal = {Acta Arithmetica},
keywords = {integers without large prime factors; short intervals; arithmetic progressions; lower bounds},
language = {eng},
number = {3},
pages = {279-289},
title = {Integers without large prime factors in short intervals and arithmetic progressions},
url = {http://eudml.org/doc/207356},
volume = {91},
year = {1999},
}

TY - JOUR
AU - Glyn Harman
TI - Integers without large prime factors in short intervals and arithmetic progressions
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 3
SP - 279
EP - 289
LA - eng
KW - integers without large prime factors; short intervals; arithmetic progressions; lower bounds
UR - http://eudml.org/doc/207356
ER -

References

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  1. [1] R. C. Baker, The greatest prime factor of the integers in an interval, Acta Arith. 47 (1986), 193-231. Zbl0553.10035
  2. [2] R. C. Baker and G. Harman, Shifted primes without large prime factors, ibid. 83 (1998), 331-361. Zbl0994.11033
  3. [3] A. Balog, p+a without large prime factors, Sém. Théorie des Nombres Bordeaux (1983-84), exposé 31. 
  4. [4] A. Balog and C. Pomerance, The distribution of smooth numbers in arithmetic progressions, Proc. Amer. Math. Soc. 115 (1992), 33-43. Zbl0752.11036
  5. [5] D. A. Burgess, On character sums and L-series, II, Proc. London Math. Soc. (3) 13 (1963), 525-536. Zbl0123.04404
  6. [6] D. A. Burgess, The character sum estimate with r=3, J. London Math. Soc. (2) 33 (1986), 219-226. Zbl0593.10033
  7. [7] J. B. Friedlander, Integers free from large and small primes, Proc. London Math. Soc. (3) 33 (1976), 565-576. Zbl0344.10021
  8. [8] J. B. Friedlander, Shifted primes without large prime factors, in: Number Theory and Applications, 1989, Kluwer, Berlin, 1990, 393-401. 
  9. [9] J. B. Friedlander and A. Granville, Smoothing `smooth' numbers, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 339-347. Zbl0795.11041
  10. [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. Zbl0606.10033
  11. [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. Zbl0713.11001
  12. [12] A. Granville, Integers, without large prime factors, in arithmetic progressions I, Acta Math. 170 (1993), 255-273. Zbl0784.11045
  13. [13] A. Granville, Integers, without large prime factors, in arithmetic progressions II, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 349-362. Zbl0792.11036
  14. [14] G. Harman, Diophantine approximation with square-free integers, Math. Proc. Cambridge Philos. Soc. 95 (1984), 381-388. Zbl0539.10025
  15. [15] G. Harman, Short intervals containing numbers without large prime factors, ibid. 109 (1991), 1-5. Zbl0724.11041
  16. [16] H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202. 
  17. [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. Zbl0808.11073
  18. [18] H.-Q. Liu and J. Wu, Numbers with a large prime factor, Acta Arith. 89 (1999), 163-187. 
  19. [19] H. L. Montgomery, Topics in Multiplicative Number Theory, Springer, 1971. Zbl0216.03501

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