Author

Haoyang Yuan

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Preprint Jul 2026

Torsion growth of rational elliptic curves over $\Z_p$-extensions of quadratic fields

Let $E/\Q$ be an elliptic curve and let $\widetilde K_p$ be the compositum of all $\Z_p$-extensions of a quadratic field $K$. We prove that $E(\widetilde K_p)_{\tors}=E(K)_{\tors}$ for $p\geq5$. For $p=3$ and imaginary quadratic $K\neq\Q(\sqrt{-3})$, torsion on each extension is determined by its intersections with the...

Shi-Song Xu, Haoyang Yuan · 0 citations

Preprint Sep 2026

A Lang-Trotter Problem for Non-Geometric Quadratic Inductions

Let $K/\mathbb Q$ be an imaginary quadratic extension and $p$ an odd prime. Write $\rho=\operatorname{Ind}_{G_K}^{G_{\mathbb Q}}\chi$, where $E/\mathbb Q_p$ is a finite extension and $\chi:G_K\to\mathcal O_E^\times$ is a continuous character. For a fixed $r\in\mathbb Z\setminus\{0\}$, let $\pi_{\rho,r}(X)$ denote the n...

Hao-Yang Yuan · 0 citations