A Weil-bound free proof of Schur's conjecture
type: Item
instance of: scholarly article
title: A Weil-bound free proof of Schur's conjecture
zbMATH Open document ID: 0904.11040
author: Peter Müller
published in: Finite Fields and their Applications
publication date: 1999-01-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 12E20
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 1199985
zbMATH Keywords: finite field
zbMATH Keywords: permutation polynomial
zbMATH Keywords: Schur's conjecture
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
OpenAlex ID: W2031968110
Wikidata QID: Q123333604
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DOI: 10.1006/FFTA.1996.0170
description: scientific article; zbMATH DE number 1199985