Name
Title | ||
|---|---|---|
Carlitz–Wan conjecture for permutation polynomials and Weil bound for curves over finite fields |
Abstract | ||
|---|---|---|
The Carlitz–Wan conjecture, which is now a theorem, asserts that for any positive integer n, there is a constant Cn such that if q is any prime power >Cn 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 Cn=n4. On the other hand, a conjecture of Mullen, which asserts essentially that one can take Cn=n(n−2) has been shown to be false. In this paper, we use a precise version of Weil 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 n2(n−2)2. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.ffa.2018.07.006 | Finite Fields and Their Applications |
Keywords | DocType | Volume |
11T06,11G20,12E20 | Journal | 54 |
ISSN | Citations | PageRank |
1071-5797 | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jasbir S. Chahal | 1 | 0 | 1.01 |
| Sudhir R. Ghorpade | 2 | 80 | 12.16 |