Polynomials with nontrivial relations between their roots

John D. Dixon

Acta Arithmetica (1997)

  • Volume: 82, Issue: 3, page 293-302
  • ISSN: 0065-1036

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John D. Dixon. "Polynomials with nontrivial relations between their roots." Acta Arithmetica 82.3 (1997): 293-302. <http://eudml.org/doc/207093>.

@article{JohnD1997,
author = {John D. Dixon},
journal = {Acta Arithmetica},
keywords = {multiplicative relation; roots; Galois group; additive relations},
language = {eng},
number = {3},
pages = {293-302},
title = {Polynomials with nontrivial relations between their roots},
url = {http://eudml.org/doc/207093},
volume = {82},
year = {1997},
}

TY - JOUR
AU - John D. Dixon
TI - Polynomials with nontrivial relations between their roots
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 3
SP - 293
EP - 302
LA - eng
KW - multiplicative relation; roots; Galois group; additive relations
UR - http://eudml.org/doc/207093
ER -

References

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  1. [1] C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Wiley, New York, 1962. 
  2. [2] J. D. Dixon and B. Mortimer, Permutation Groups, Springer, New York, 1996. Zbl0951.20001
  3. [3] M. Drmota and M. Ska/lba, Relations between polynomial roots, Acta Arith. 71 (1995), 65-77. 
  4. [4] R. Ferguson, Irreducible polynomials with many roots of equal modulus, ibid. 78 (1997), 221-225. Zbl0867.11012
  5. [5] C. J. Smyth, Conjugate algebraic numbers on conics, ibid. 40 (1982), 333-346. Zbl0431.12001
  6. [6] C. J. Smyth, Additive and multiplicative relations connecting conjugate algebraic numbers, J. Number Theory 23 (1986), 243-254. Zbl0586.12001
  7. [7] N. Tschebotaröw, Grundzüge der Galoisschen Theorie (transl. and revised by H. Schwerdtfeger), Noordhoff, Groningen, 1950. Zbl0037.14602
  8. [8] B. L. van der Waerden, Modern Algebra, Vol. I, Ungar, New York, 1948. 
  9. [9] H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964. 

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