Lenstra's Proof of the Carlitz-Wan Conjecture on Exceptional Polynomials: An Elementary Version

Authors:
S. D. Cohen;M. D. Fried
Affiliations:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland and Department of Mathematics, University of California, Irvine, California 92717;Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland and Department of Mathematics, University of California, Irvine, California 92717
Venue:
Finite Fields and Their Applications
Year:
1995

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Abstract

We give a proof, following an argument of Lenstra, of the conjecture of Carlitz (1966) as generalized by Wan (1993). This says that there are no exceptional polynomials of degree n over F"q if (n, q - 1) 1. Fried, Guralnick, and Saxl previously proved Carlitz's conjecture: there are no exceptional polynomials of even degree over fields of odd order.