Fields generated by linear combinations of roots of unity
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- by R. J. Evans and I. M. Isaacs
- Trans. Amer. Math. Soc. 229 (1977), 249-258
- DOI: https://doi.org/10.1090/S0002-9947-1977-0437509-2
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Abstract:
It is shown that a linear combination of roots of unity with rational coefficients generates a large subfield of the field generated by the set of roots of unity involved, except when certain partial sums vanish. Some related results about polygons with all sides and angles rational are also proved.References
- R. Bercov and L. Moser, On Abelian permutation groups, Canad. Math. Bull. 8 (1965), 627–630. MR 190217, DOI 10.4153/CMB-1965-045-6
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 229 (1977), 249-258
- MSC: Primary 12F05
- DOI: https://doi.org/10.1090/S0002-9947-1977-0437509-2
- MathSciNet review: 0437509