Smoothing \smooth" Numbers Smoothing \smooth" Numbers

@inproceedings{Friedlander2007SmoothingN,
  title={Smoothing \smooth" Numbers Smoothing \smooth" Numbers},
  author={NumbersJohn B. Friedlander},
  year={2007}
}
  • NumbersJohn B. Friedlander
  • Published 2007
An integer is called y-smooth if all of its prime factors are y. An important problem is to show that the y-smooth integers up to x are equi-distributed amongst short intervals. In particular, for many applications we would like to know that if y is an arbitrarily small, xed power of x then all intervals of length p x, up to x, contain, asymptotically, the same number of y-smooth integers. We come close to this objective by proving that such y-smooth integers are so equi-distributed in… CONTINUE READING

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 10 references

On the distribution in short intervals of integers

J. B. Friedlander, J. C. Lagarias
1987
View 7 Excerpts
Highly Influenced

On the distribution in short intervals of integershaving no large prime factor

J. B. Friedlander, J. C. Lagarias
J . Number Theory • 1987
View 4 Excerpts
Highly Influenced

On the distribution of integers having no large prime factor

A. Balog
1987
View 5 Excerpts
Highly Influenced

ON THE abc CONJECTURE , II

C. L. Stewart, YU KUNRUI
2001
View 1 Excerpt

Short intervals containing numbers without large prime factors

G. Harman
Math . Proc . Cambridge Phil . Soc . • 1991

On the number of positive integers x and free of prime factors > y

A. Hildebrand
J . Number Theory • 1986
View 2 Excerpts

Integers free of large prime factors in short intervals

A. Hildebrand
Quart J. Math • 1985
View 1 Excerpt

On integers with many small prime factors

R. Tijdeman
Comp. Math • 1973
View 1 Excerpt

Similar Papers

Loading similar papers…