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A Weil-Bound Free Proof of Schur's Conjecture

✍ Scribed by Peter Müller

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
226 KB
Volume
3
Category
Article
ISSN
1071-5797

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✦ Synopsis

Let f be a polynomial with coefficients in the ring O K of integers of a number field. Suppose that f induces a permutation on the residue fields O K /ᒍ for infinitely many nonzero prime ideals ᒍ of O K . Then Schur's conjecture, namely that f is a composition of linear and Dickson polynomials, has been proved by M. Fried. All the present versions of the proof use Weil's bound on the number of points of absolutely irreducible curves over finite fields in order to get a Galois theoretic translation and to finish the proof by means of finite group theory. This note replaces the use of this deep result by elementary arguments.

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