On a problem concerning permutation polynomials
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- by Gerhard Turnwald PDF
- Trans. Amer. Math. Soc. 302 (1987), 251-267 Request permission
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
- Michael Fried, On a conjecture of Schur, Michigan Math. J. 17 (1970), 41–55. MR 257033
- Gerald J. Janusz, Algebraic number fields, Pure and Applied Mathematics, Vol. 55, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. MR 0366864 H. Lausch and W. Nöbauer, Algebra of polynomials, North-Holland, Amsterdam, 1973.
- Władysław Narkiewicz, Uniform distribution of sequences of integers in residue classes, Lecture Notes in Mathematics, vol. 1087, Springer-Verlag, Berlin, 1984. MR 766563, DOI 10.1007/BFb0100180
- H. Niederreiter and Siu Kwong Lo, Permutation polynomials over rings of algebraic integers, Abh. Math. Sem. Univ. Hamburg 49 (1979), 126–139. MR 549201, DOI 10.1007/BF02950653
- W. Nöbauer, Polynome, welche für gegebene Zahlen Permutationspolynome sind, Acta Arith. 11 (1966), 437–442 (German). MR 202702, DOI 10.4064/aa-11-4-437-441 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.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 302 (1987), 251-267
- MSC: Primary 11T06; Secondary 11R99
- DOI: https://doi.org/10.1090/S0002-9947-1987-0887508-8
- MathSciNet review: 887508