Author

Ming-Hsuan Kang

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Preprint Aug 2026

Quadratic-Defect Completions of Spherical $2$-Design Orbits

We study how spherical $2$-designs arising from finite group orbits can be completed to spherical $4$-designs by adjoining further orbits, allowing weights in the general theory. For an irreducible real orthogonal $G$-module $W$ with $\mathbb D=\operatorname{End}_G(W)\in\{\mathbb R,\mathbb C,\mathbb H\}$, we consider t...

Kuan-Chen Chien, Ming-Hsuan Kang · 0 citations

Preprint Aug 2026

Ramanujan Cayley Graphs with Normal Connection Sets in Ratio-One Frobenius Groups

Let $G=N\rtimes H$ be a finite Frobenius group with $|N|=q$ and $|H|=q-1$. We classify all Ramanujan Cayley graphs of $G$ whose connection sets are normal, in the sense of being unions of conjugacy classes. The group-theoretic input is a simple blow-up phenomenon: every such Cayley graph is either $Y[\overline{K_q}]$ o...

Ming-Hsuan Kang, Chi-Jung Yang · 0 citations

Preprint Jul 2026

Zeta functions of $\mathrm{PGL}_n$ over non-Archimedean local fields

Let $\mathscr{B}$ be the Bruhat--Tits building of $\mathrm{PGL}_n(F)$, where $F$ is a non-Archimedean local field. We introduce geometric $k$-geodesics in $\mathscr{B}$ by means of CAT(0) convexity and combinatorial $k$-geodesics by a local successor relation on pointed $k$-facets. We prove that the two notions coincid...

Ming-Hsuan Kang, Jiu-Kang Yu · 0 citations