Abstract
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 among short intervals. In particular, for many applications we would like to know that if
y
is an arbitrarily small, fixed power of
x
then all intervals of length
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 intervals of length
x
y
2
+
ε
, for any fixed ε < 0.
Subject
Pharmacology (medical),Complementary and alternative medicine,Pharmaceutical Science
Cited by
7 articles.
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