Permutation polynomials and resolution of singularities over finite fields
Da Qing Wan · Proceedings of the American Mathematical Society · 1990
A geometric approach is introduced to study permutation polynomials over a finite field. As an application, we prove that there are no permutation polynomials of degree 2 l 2l over a large finite field, where l l is an odd prime. This proves that the Carlitz conjecture is true for n = 2 l n = 2l . Previously, the conjecture was known to be true only for n ≤ 16 n \leq 16 .