Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On a problem concerning permutation polynomials

Author: Gerhard Turnwald
Journal: Trans. Amer. Math. Soc. 302 (1987), 251-267
MSC: Primary 11T06; Secondary 11R99
MathSciNet review: 887508
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ S(f)$ denote the set of integral ideals $ I$ such that $ f$ is a permutation polynomial modulo $ I$, where $ f$ is a polynomial over the ring of integers of an algebraic number field. We obtain a classification for the sets $ S$ which may be written in the form $ S(f)$.

References [Enhancements On Off] (What's this?)

  • [1] Michael Fried, On a conjecture of Schur, Michigan Math. J. 17 (1970), 41–55. MR 0257033
  • [2] Gerald J. Janusz, Algebraic number fields, Academic Press [A Subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1973. Pure and Applied Mathematics, Vol. 55. MR 0366864
  • [3] H. Lausch and W. Nöbauer, Algebra of polynomials, North-Holland, Amsterdam, 1973.
  • [4] Władysław Narkiewicz, Uniform distribution of sequences of integers in residue classes, Lecture Notes in Mathematics, vol. 1087, Springer-Verlag, Berlin, 1984. MR 766563
  • [5] H. Niederreiter and Siu Kwong Lo, Permutation polynomials over rings of algebraic integers, Abh. Math. Sem. Univ. Hamburg 49 (1979), 126–139. MR 549201, 10.1007/BF02950653
  • [6] W. Nöbauer, Polynome, welche für gegebene Zahlen Permutationspolynome sind, Acta Arith. 11 (1966), 437–442 (German). MR 0202702
  • [7] I. Schur, Über den Zusammenhang zwischen einem Problem der Zahlentheorie und einem Satz über algebraische Funktionen, S.-B. Preuss. Akad. Wiss. Berlin (1923), 123-134.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11T06, 11R99

Retrieve articles in all journals with MSC: 11T06, 11R99

Additional Information

Keywords: Permutation polynomials, Dickson-polynomials, Schur's conjecture, algebraic integers
Article copyright: © Copyright 1987 American Mathematical Society