Author

Shi-Song Xu

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Preprint Sep 2026

Positivity and Asymptotics for Chenevier's Orthogonal Polynomials

We prove the strict positivity conjectured by Chenevier for the critical vectors in the unconditional part of his automorphic Hermite--Minkowski theorem. The proof establishes strict negativity of all Verblunsky coefficients of a circle measure associated with the weight $(\arcsin x)/x$ on $(-1,1)$. A positive-kernel f...

Shi-Song Xu · 0 citations

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