# Relations between polynomial roots

Michael Drmota; Mariusz Skałba

Acta Arithmetica (1995)

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

## Access Full Article

top## How to cite

topMichael 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

top- [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] 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] 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] T. Hawkins, The origins of the theory of group characters, Arch. Hist. Exact Sci. 7 (1971), 142-170.
- [5] H. B. Mann, On linear relations between roots of unity, Mathematika 12 (1965), 107-117. Zbl0138.03102
- [6] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Springer, Berlin, 1990. Zbl0717.11045
- [7] A. Schinzel, On the reducibility of polynomials and in particular of trinomials, Acta Arith. 11 (1965), 1-34.
- [8] C. J. Smyth, Additive and multiplicative relations connecting conjugate algebraic numbers, J. Number Theory 23 (1986), 243-254. Zbl0586.12001
- [9] C. J. Smyth, Conjugate algebraic numbers on conics, Acta Arith. 40 (1982), 333-346 Zbl0431.12001

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.