A new family of exceptional polynomials in characteristic two | Annals of Mathematics

Abstract We produce a new family of polynomials f(X) over fields k of characteristic 2 which are exceptional, in the sense that f(X)−f(Y) has no absolutely irreducible factors in k[X,Y] except for scalar multiples of X−Y; when k is finite, this condition is equivalent to saying that the map α↦f(α) induces a bijection on an infinite algebraic extension of k. Our polynomials have degree 2e−1(2e−1), where e>1 is odd. We also prove that this completes the classification of indecomposable exceptional polynomials of degree not a power of the characteristic.

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数学年刊（Annals of Mathematics）

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