On the discriminants of truncated logarithmic polynomials

Abstract

We provide evidence for a conjecture of Yamamura that the truncated logarithmic polynomials \[ F_n(x) = 1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n} \] have Galois group $S_n$ for all $n \geq 1$.