Author

Liming Ma

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Preprint Sep 2026

A new family of maximal curves not covered by the Hermitian curve

For every prime power $q$ and integer $n\ge1$, we give a single Kummer equation defining an $\mathbb{F}_{q^{2n}}$-maximal curve $\mathcal X_{q,n}$. The family recovers the Hermitian curves for $n=1,2$, the Giulietti--Korchm\'aros curve for $n=3$, and the Beelen--Montanucci curves for odd $n\ge5$. For $q>2$ and even $n\...

Li-Ming Ma, Yi-Peng Wang · 0 citations

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 Sep 2026

Explicit equations of Galois subfields of Hermitian function fields with respect to decomposition groups

Let $q$ be a prime power and $\mathbb{F}_{q^2}$ be the finite fields of $q^2$ elements. The Hermitian function field $H=\mathbb{F}_{q^2}(x,y)$ defined by $y^q+y=x^{q+1}$ is a well-known maximal function field with the largest possible genus. Let $A(P_\infty)$ be the decomposition group of the infinity place $P_\infty$...

Li-Ming Ma, Yi-Peng Wang · 2 citations