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ON IRREDUCIBILITY OF COMPOSITION POLYNOMIALS

  • Choi, EunMi (Department of Mathematics HanNam University)
  • Received : 2011.06.27
  • Accepted : 2011.11.18
  • Published : 2011.12.30

Abstract

We investigate the irreducibility of iterate and composite polynomials. For this purpose discriminant and resultant are computed by means of the norm function.

Keywords

References

  1. R. Jones, The density of prime divisors in the arithmetic dynamics of quadratic polynomials, J. London Math. Soc. (2), 78 (2008), no. 2, 523-544. https://doi.org/10.1112/jlms/jdn034
  2. J. H. McKay, S. S. Wang. A chain rule for the resultant of two polynomials, Arch. Math. 53 (4). (1989) 347-351. https://doi.org/10.1007/BF01195214
  3. R. K. W. Odoni, The Galois theory of iterates and composites of polynomials, Prod. London Math Soc. (3), 51 (1985), no. 3, 385-414. https://doi.org/10.1112/plms/s3-51.3.385
  4. J. R. Bastida, Field extensions and Galois theory, Encyclopedia of Mathematics and its applications, 22, Addison-Wesley Publishing Company, 1984.
  5. R. G. Swan, Factorization of polynomials over finite field, Pacific Journal of Mathematics 12 (1962), 1099-1106. https://doi.org/10.2140/pjm.1962.12.1099
  6. J. J. Sylvester, On a general method of determining by mere inspection the derivation from two equations of any degree, Philosophical Magazine 16 (1840), 132-135.