Zhi-Chao Tang

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math.NT2026

Wendt's determinant and finiteness of prime characteristics for permutation binomials

Zhichao Tang, Xiang Fan

For $f (X) = X^{r} (X^{s} + a) \in F_{p^{m}} [X]$ , with $m, r, s ⩾ 1$ and $a \in F_{p^{m}}^{\times}$ , put $g = g cd (s, p^{m} - 1)$ . We prove that, for each fixed $g$ , only finitely many pr…

math.NT2026

Shifted dihedral isogeny quotients and the classification of exceptional rational functions of degree five

Zhichao Tang, Xiang Fan

We give a complete classification, up to $k$ -Möbius equivalence, of exceptional rational functions of degree five over every finite field. The classification gives explicit normal…