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

The authors requested a withdrawal of this article shortly after it first appeared in press in 2014. Unfortunately, the withdrawal was implemented as a retraction instead by the publisher and an earlier version of this notice contained allegations in relation to the article that, following further editorial consideration, the journal has found to be incorrect. The Publisher apologizes to the authors and has now re-published the article with minor changes at https://doi.org/10.1016/j.ffa.2018.07.006.

[1]  Sudhir R. Ghorpade,et al.  \'Etale cohomology, Lefschetz Theorems and Number of Points of Singular Varieties over Finite Fields , 2008, 0808.2169.

[2]  G. Mullen Permutation Polynomials , 1995 .

[3]  David B. Leep,et al.  The number of points on a singular curve over a finite field , 1994 .

[4]  Kenneth S. Williams,et al.  On Exceptional Polynomials , 1968, Canadian Mathematical Bulletin.

[5]  K. Conrad,et al.  Finite Fields , 2018, Series and Products in the Development of Mathematics.

[6]  A. Weil Sur les courbes algébriques et les variétés qui s'en déduisent , 1948 .

[7]  David R. Hayes A geometric approach to permutation polynomials over a finite field , 1967 .

[8]  Cunsheng Ding,et al.  Permutation polynomials over finite fields from a powerful lemma , 2011, Finite Fields Their Appl..

[9]  Robert M. Guralnick,et al.  Schur covers and Carlitz’s conjecture , 1993 .

[10]  Ariane M. Masuda,et al.  Permutation binomials over finite fields , 2007, 0707.1108.

[11]  Yves Aubry,et al.  A Weil theorem for singular curves , 1996 .

[12]  Guillermo Matera,et al.  Improved explicit estimates on the number of solutions of equations over a finite field , 2006, Finite Fields Their Appl..

[13]  Wang Daqing On a Conjecture of Carlitz , 1987, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[14]  S. D. Cohen,et al.  Lenstra's Proof of the Carlitz-Wan Conjecture on Exceptional Polynomials , 1995 .

[15]  Stephen D. Cohen,et al.  The distribution of polynomials over finite fields , 1970 .

[16]  Joachim von zur Gathen,et al.  Values of polynomials over finite fields , 1991, Bulletin of the Australian Mathematical Society.

[17]  G. Turnwald A New Criterion for Permutation Polynomials , 1995 .

[18]  С. R. MacCluer On a conjecture of Davenport and Lewis concerning exceptional polynomials , 1967 .

[19]  Eric Bach,et al.  Weil bounds for singular curves , 1996, Applicable Algebra in Engineering, Communication and Computing.

[20]  Sudhir R. Ghorpade,et al.  A Course in Multivariable Calculus and Analysis , 2009 .

[21]  Wang Daqing,et al.  Permutation polynomials over finite fields , 1987 .

[22]  Rudolf Lide,et al.  Finite fields , 1983 .

[23]  Gary L. Mullen,et al.  Finite fields, coding theory, and advances in communications and computing , 1993 .

[24]  Ian M. Wanless,et al.  Permutation polynomials and orthomorphism polynomials of degree six , 2013, Finite Fields Their Appl..

[25]  Sudhir R. Ghorpade,et al.  Singular Varieties over Finite Fields , 2002 .