J Austral Math Soc Ser A 58 pp312--357, 1995.

On Schur's Conjecture

Gerhard Turnwald

(Received 4 March 1992; revised 30 June 1992)

Abstract

We study polynomials over an integral domain R which, for infinitely many prime ideals P, induce a permutation of R/P. In many cases, every polynomial with this property must be a composition of Dickson polynomials and of linear polynomials with coefficients in the quotient field of R. In order to find out which of these compositions have the required property we investigate some number theoretic aspects of composition of polynomials. The paper includes a rather elementary proof of 'Schur's Conjecture' and contains a quantitative version for polynomials of prime degree.

1991 AMS Subject Classification: 11T06, 12E05

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Authors

Gerhard Turnwald: Mathematisches Institut der Universitat, Auf der Morganstelle 10, d-72076 Tubingen, Germany.

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Last Modified: Thu Jan 9 9:04:22 2003