Analytic rank-one elliptic curves over function fields and their rank over certain ring class fields

Seokhyun Choi, Bo-Hae Im, Beomho Kim

Let $E/k$ be a non-isotrivial elliptic curve over a global function field $k$ of characteristic $p>3$, and $G\subset \mathrm{Gal}(k^{\mathrm{sep}}/k)$ be a topologically finitely g…