The Distribution of Smooth Numbers in Arithmetic Progressions

Abstract

We estimate the number of integers $n$ up to $x$ in the arithmetic progression $a(\bmod q)$ with $n$ free of prime factors exceeding $y$. For a wide range of the variables $x,y,q$, and $a$ we show that this number is about $x/(q{u^u})$, where $u = \log x/\log y$.

Locations

• Proceedings of the American Mathematical Society - View - PDF