Author

Zugan Xing

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Preprint Oct 2026

Zassenhaus Filtration and Ihara Constants

Let $X$ be a curve over $\mathbb{F}_q$. Denote by $N(X)$ and $g(X)$ the number of $\mathbb{F}_q$-rational points and the genus of $X$ respectively. The Ihara constant \begin{equation*} A(q)=\limsup_{g(X)\to\infty}\frac{N(X)}{g(X)} \end{equation*} measures the asymptotic abundance of rational points on curves over $\mat...

Li-Ming Ma, Chao-Ping Xing, Zu-Gan Xing · 0 citations

Preprint Aug 2026

Multiplicator freeness for restricted-ramification Galois groups over global function fields

Let $K$ be a global function field with full constant field $\mathbb{F}_q$, let $T$ be a finite set of finite places, and let $\infty$ be a distinguished place. We study the maximal pro-$\ell$ extension of $K$ which is unramified outside $T$ and in which $\infty$ splits completely. Using factorisation results for $\ell...

Qi Liu, Zugan Xing · 0 citations