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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Permutation polynomials and resolution of singularities over finite fields


Author: Da Qing Wan
Journal: Proc. Amer. Math. Soc. 110 (1990), 303-309
MSC: Primary 11T06
DOI: https://doi.org/10.1090/S0002-9939-1990-1031673-4
MathSciNet review: 1031673
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Abstract: A geometric approach is introduced to study permutation polynomials over a finite field. As an application, we prove that there are no permutation polynomials of degree $ 2l$ over a large finite field, where $ l$ is an odd prime. This proves that the Carlitz conjecture is true for $ n = 2l$. Previously, the conjecture was known to be true only for $ n \leq 16$.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1031673-4
Article copyright: © Copyright 1990 American Mathematical Society