Smoothing \smooth" Numbers Smoothing \smooth" Numbers

  title={Smoothing \smooth" Numbers Smoothing \smooth" Numbers},
  author={NumbersJohn B. Friedlander},
  • 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


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