| Reference: | [1] Wayne Aitken, On value sets of polynomials over a finite field, Preprint (1997).
[2] L. Carlitz, D. J. Lewis, W. H. Mills and E. G. Straus, Polynomials over finite fields with minimal value set, Mathematika 8(1961), 121-130.
[3] L. Carlitz and J. A. Lutz, A characterization of permutation polynomials over a finite field, American Mathematical Monthly 85(1978), 746-748.
[4] S. D. Cohen, The distribution of polynomials over finite fields, Acta Arithmetica 17(1970), 255-271.
[5] H. Davenport and D. J. Lewis, Note on congruences (I), Quarterly Journal of Mathematics 14(1963), 51-60.
[6] L. E. Dickson, The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group, Annals of Mathematics 11(1897), 65-120, 161-183.
[7] J. Gomez-Calderon, A note on polynomials with minimal value set over finite field, Mathematika 35(1988), 144-148.
[8] J. Gomez-Calderon, and D. J. Madden, Polynomials with small value set over finite fields, Journal of Number Theory 28(1988), 167-188.
[9] J. von zur Gathen, Values of polynomials over finite fields, Bulletin of Australian Mathematical Society 43(1991), 141-146.
[10] D. R. Hayes, A geometric approach to permutation polynomials over a finite field, Duke Mathematical Journal 34(1967), 293-305.
[11] C. Hermite, Sur les fonctions de sept letters, Comptes Rendus de L` Academie des Sciences, Paris, 57(1863), 750-757; Oeuvres, vol 2, Gauthier-Villars, Paris, 1908, 280-288.
[12] N. Koblitz, p-adic analysis: a short course on recent work, Cambridge University Press, 1980.
[13] S. Lang, Linear Algebra, third edition by Springer-Verlag New York Inc. 1987.
[14] J. Levine and J. V. Brawley, Some cryptographic applications of permutation polynomials, Cryptologia 1(1977), 76-92.
[15] R. Lidl and G. L. Mullen, When does a polynomial over a finite field permute the elements of the field, American Mathematical Monthly 95(1988), 243-246.
[16] R. Lidl and G. L. Mullen, When does a polynomial over a finite field permute the elements of the field? 2, American Mathematical Monthly 100(1993), 71-74.
[17] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of mathematics and its applications, Vol 20, first published by Addison-Wesley Publishing Inc. 1983, and second edition published by Cambridge University Press 1997.
[18] C. R. MacCluer, On a conjecture of Davenport and Lewis concerning exceptional polynomials, Acta Arithmetica 12(1967), 289-299.
[19] W. H. Mills, Polynomials with minimal value sets, Pacific Journal of Mathematics 14(1964), 225-241.
[20] G. L. Mullen, Permutation polynomials over finite fields, Proceedings of international conference on finite fields, coding theory and advences in communications and computing, lecture notes in Pure and Applied Mathematika, vol 141, Marcel Dekker, New York, 1992, 131-151.
[21] G. L. Mullen, Permutation polynomials: A matrix analogue of Schur`s conjecture and a survey of recent result, Finite Fields and Their Applications 1, 1995, 242-258.
[22] G. Turnwald, A new criterion for permutation polynomials, Finite Fields and Their Applications 1, 1995, 64-82.
[23] D. Wan, On a conjecture of Carlitz, Journal of Australian Mathematical Society, Series A 43(1987), 375-384.
[24] D. Wan, A p-adic lifting lemma and its applications to permutation polynomials, Proceedings of the international conference on finite fields, coding theory and advances in communication and computing, lecture notes in Pure and Applied Mathematika, vol 141, Marcel Dekker, New York, 1993, 209-216.
[25] D. Wan, A generalization of Carlitz conjecture, Proceedings of the international conference on finite fields, coding theory and advances in communication and computing, lecture notes in Pure and Applied Mathematika, vol 141, Marcel Dekker, New York, 1993, 431-432.
[26] D. Wan, G. L. Mullen and P. J.-S. Shiue, The number of permutation polynomials of the form f(x)+cx over a finite field, Proceedings Edinburgh Mathematical Society, 38(1995), 133-149.
[27] D. Wan, P. J.-S. Shiue, and C.-S. Chen, Value sets of polynomial over finite fields, Proceedings of the American Mathematical Society 119(1993), 711-717.
[28] K. S. Williams, On exceptional polynomials, Canadian Mathematical Bulletin 11(1968), 279-282. |
