Year: 2026
Type: preprint
Abstract: Let $\mathbf{E}$ be the ring of values taken at algebraic points by $E$-functions. The exponential function and the Bessel function $J_0$ are classical examples of $E$-functions. We prove that $\mathbf{E}$ is not a field. More precisely, we prove that it is neither noetherian nor factorial, and construct non-units of $\mathbf{E}$ explicity, including $e+1$, $J_0(1)$, and ${}_1F_1(a;b;1)$ for rational parameters $a$ and $b$ such that $0
Source: arXiv (Cornell University)
Authors: Fischler, Stéphane, Rivoal, Tanguy
Institution: Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214568397