Year: 2026
Type: preprint
Abstract: Consider the shifted truncations of the exponential series and their Galois groups: $$F_{n,a}(x) := \sum_{j=0}^{n}\frac{x^j}{(a+j)!}\qquad G_{n,a}:= \text{Gal}(F_{n,a}/\mathbb{Q}).$$ In this paper we prove that for every fixed integer $a>0$, the set of $n$ for which $G_{n,a}=S_n$ has natural density one, thus answering a question of Katz and Rivin.
Source: arXiv (Cornell University)
Author: Weinbaum, Shachar
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Princeton University, Tel Aviv University
OpenAlex ID: W7220407380