Relations between polynomial roots

Michael Drmota; Mariusz Skałba

Acta Arithmetica (1995)

  • Volume: 71, Issue: 1, page 65-77
  • ISSN: 0065-1036

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Michael Drmota, and Mariusz Skałba. "Relations between polynomial roots." Acta Arithmetica 71.1 (1995): 65-77. <http://eudml.org/doc/270184>.

@article{MichaelDrmota1995,
author = {Michael Drmota, Mariusz Skałba},
journal = {Acta Arithmetica},
keywords = {polynomial roots; Tschirnhausen transformation; multiplicative relations; roots of rational polynomials; abelian splitting fields; abelian Galois group},
language = {eng},
number = {1},
pages = {65-77},
title = {Relations between polynomial roots},
url = {http://eudml.org/doc/270184},
volume = {71},
year = {1995},
}

TY - JOUR
AU - Michael Drmota
AU - Mariusz Skałba
TI - Relations between polynomial roots
JO - Acta Arithmetica
PY - 1995
VL - 71
IS - 1
SP - 65
EP - 77
LA - eng
KW - polynomial roots; Tschirnhausen transformation; multiplicative relations; roots of rational polynomials; abelian splitting fields; abelian Galois group
UR - http://eudml.org/doc/270184
ER -

References

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  1. [1] J. H. Conway and A. J. Jones, Trigonometric diophantine equations (On vanishing sums of roots of unity), Acta Arith. 30 (1976), 229-240. Zbl0349.10014
  2. [2] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401. Zbl0416.12001
  3. [3] M. Drmota and M. Skałba, On multiplicative and linear independence of polynomial roots, in: Contributions to General Algebra 7, D. Dorninger, G. Eigenthaler, H. K. Kaiser and W. B. Müller (eds.), Hölder-Pichler-Tempsky, Wien, and Teubner, Stuttgart, 1991, 127-135. 
  4. [4] T. Hawkins, The origins of the theory of group characters, Arch. Hist. Exact Sci. 7 (1971), 142-170. 
  5. [5] H. B. Mann, On linear relations between roots of unity, Mathematika 12 (1965), 107-117. Zbl0138.03102
  6. [6] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Springer, Berlin, 1990. Zbl0717.11045
  7. [7] A. Schinzel, On the reducibility of polynomials and in particular of trinomials, Acta Arith. 11 (1965), 1-34. 
  8. [8] C. J. Smyth, Additive and multiplicative relations connecting conjugate algebraic numbers, J. Number Theory 23 (1986), 243-254. Zbl0586.12001
  9. [9] C. J. Smyth, Conjugate algebraic numbers on conics, Acta Arith. 40 (1982), 333-346 Zbl0431.12001

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