A proof of van der Waerden's Conjecture on random Galois groups of polynomials

Manjul Bhargava

Of the $(2H+1{)}^n$ monic integer polynomials $f(x)=x^n+a_1{x}^{n-1}+\cdots +a_n$ with $\max \{|a_1|,\dots ,|a_n|\}\le H$, how many have associated Galois group that is not the full sy…