PreprintCC BY-SA 4.0arXiv
Galois Groups of Shifted Exponential Polynomials
Abstract
Consider the shifted truncations of the exponential series and their Galois groups: Fn,a(x) := ∑j=0nxj/((a+j)!) Gn,a:= Gal(Fn,a/ℚ). In this paper we prove that for every fixed integer a>0, the set of n for which Gn,a=Sn has natural density one, thus answering a question of Katz and Rivin.
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BibTeX
@misc{weinbaum2026galois,
title = {{Galois Groups of Shifted Exponential Polynomials}},
author = {Shachar Weinbaum},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26873},
eprint = {2610.26873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26873},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Galois Groups of Shifted Exponential Polynomials
AU - Shachar Weinbaum
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.26873
UR - https://arxiv.org/abs/2610.26873
AB - Consider the shifted truncations of the exponential series and their Galois groups: F_n,a(x) := ∑_j=0^nx^j/((a+j)!) G_n,a:= Gal(F_n,a/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.
ER -