Year: 2026
Type: preprint
Abstract: Recent work of Bergeron-Charollois-García proposed a conjectural analytic expression for elliptic units for complex cubic fields as the special values of smoothed quotients of elliptic Gamma functions. These values depend on the conductor ideal, ray class group element, smoothing ideal, and an admissible element $h$. If this analytic expression is to fit into the framework of explicit class field theory, then, as in the case of torsion points on CM elliptic curves, the resulting complex number should depend only on the congruence class of $h$ modulo a fractional ideal. This conjecture has been supported by much numerical evidence. In this paper, we use the cocycle relations of the smoothed elliptic Gamma function to prove that the construction is indeed independent of $h$.
Source: arXiv (Cornell University)
Author: Gray, Teymour
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221047522