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math.NT2025
Determination of all complete mappings of F_{q^2} of the form aX^{3q}+bX^{2q+1}+cX^{q+2}+dX^3
Zhiguo Ding, Wei Xiong, Michael E. Zieve
For each prime power q, we determine all polynomials over F_{q^2} of the form f(X) := aX^{3q}+bX^{2q+1}+cX^{q+2}+dX^3 which induce complete mappings of F_{q^2}, in the sense that e…
math.NT2025
Exceptional extensions of local fields and the Carlitz--Wan conjecture
Zhiguo Ding, Wei Xiong, Qifan Zhang
For any prime power , a polynomial $f(X)\in\F_q[X]$ is ``exceptional'' if it induces bijections of $\F_{q^k}$ for infinitely many ; this condition is known to be equivalent t…
math.NT2025
Some classes of permutation pentanomials
Zhiguo Ding, Michael E. Zieve
For each prime p other than 3, and each power q=p^k, we present two large classes of permutation polynomials over F_{q^2} of the form X^r B(X^{q-1}) which have at most five terms,…