A Weil-bound free proof of Schur's conjecture
Let \({\mathfrak O}_K\) be the ring of integers of an algebraic number field \(K\) and let \(f(x)\in {\mathfrak O}_K[x]\). Suppose that \(f\) is a permutation polynomial over \({\mathfrak O}_K/{\mathfrak p}\). \textit{M. Fried} [Mich. Math. J. 17, 41-55 (1970; Zbl 0169.37702)] proved that \(f\) is a composition of linear Dickson polynomials, known as Schur's conjecture. This proof, and all others prior to this, use Weil's bound on the number of points of absolutely irreducible curves over finite fields. The paper under review replaces the Weil bound with elementary arguments.
scientific article; zbMATH DE number 1199985