Year: 2026
Type: preprint
Abstract: We determine thirteen entirely CM identity fibers of Shimura parametrizations attached to elliptic curves of rank two and conductor below $2000$. Each yields a proof of the imaginary quadratic class number one theorem. The argument combines the Gross--Zagier formula with the Ribet--Takahashi degree comparison to show that the fiber is completely explained by known CM points.
Source: arXiv (Cornell University)
Author: Geng, Jingxuan
Institution: The Ohio State University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221817407