Squarefree quartics and power-free polynomial values
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The formalized result proves positive-density power-free values for every integer polynomial $f$ irreducible over $\mathbb Q$ of degree $d\ge4$. Put $k=d-2$ and assume no prime $k$th power divides every value of $f$. Then the number of positive integers $n\le X$ for which $f(n)$ is $k$-free is $c_fX+o_f(X)$, where $c_f>0$ is the convergent product of local factors. Negative values are allowed and zero is excluded. No monicity, primitivity, or coefficient-height restriction is imposed.
Comparator links
| Result | Comparator statement |
|---|---|
| Positive density of power-free polynomial values | PowerFreeValues.lean |