# Smoothing \smooth" Numbers Smoothing \smooth" Numbers

@inproceedings{Friedlander2007SmoothingN, title={Smoothing \smooth" Numbers Smoothing \smooth" Numbers}, author={NumbersJohn B. Friedlander}, year={2007} }

- 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.

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#### References

##### Publications referenced by this paper.

Showing 1-10 of 10 references

## On the distribution in short intervals of integers

View 7 Excerpts

Highly Influenced

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

View 4 Excerpts

Highly Influenced

## On the distribution of integers having no large prime factor

View 5 Excerpts

Highly Influenced

## ON THE abc CONJECTURE , II

View 1 Excerpt

## Short intervals containing numbers without large prime factors

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

View 2 Excerpts

## Integers free of large prime factors in short intervals

View 1 Excerpt

## On integers with many small prime factors

View 1 Excerpt