Galois groups of reciprocal polynomials and the van der Waerden-Bhargava
theorem
Galois groups of reciprocal polynomials and the van der Waerden-Bhargava
theorem
We study the Galois groups $G_f$ of degree $2n$ reciprocal (a.k.a. palindromic) polynomials $f$ of height at most $H$, finding that $G_f$ falls short of the maximal possible group $S_2 \wr S_n$ for a proportion of all $f$ bounded above and below by constant multiples of $H^{-1} \log H$, whether …