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Carlitz-Wan conjecture for permutation polynomials and Weil bound for curves over finite fields

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Title Carlitz-Wan conjecture for permutation polynomials and Weil bound for curves over finite fields
 
Creator CHAHAL, JS
GHORPADE, SR
 
Subject Permutation polynomial
Exceptional polynomial
Separable polynomial
Weil bound
NUMBER
 
Description The Carlitz-Wan conjecture, which is now a theorem, asserts that for any positive integer n, there is a constant C-n such that if q is any prime power > C-n with GCD(n, q - 1) > 1, then there is no permutation polynomial of degree n over the finite field with q elements. From the work of von zur Gathen, it is known that one can take C-n = n(4). On the other hand, a conjecture of Mullen, which asserts essentially that one can take C-n = n(n - 2) has been shown to be false. In this paper, we use a precise version of Well bound for the number of points of affine algebraic curves over finite fields to obtain a refinement of the result of von zur Gathen where n4 is replaced by a sharper bound. As a corollary, we show that Mullen's conjecture holds in the affirmative if n(n - 2) is replaced by n(2) (n - 2)(2). (C) 2014 Elsevier Inc. All rights reserved.
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2014-12-28T11:08:53Z
2014-12-28T11:08:53Z
2014
 
Type Article
 
Identifier FINITE FIELDS AND THEIR APPLICATIONS, 28282-291
1071-5797
1090-2465
http://dx.doi.org/10.1016/j.ffa.2014.03.001
http://dspace.library.iitb.ac.in/jspui/handle/100/16320
 
Language English