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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Fields generated by linear combinations of roots of unity


Authors: R. J. Evans and I. M. Isaacs
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
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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 [Enhancements On Off] (What's this?)

  • [1] R. Bercov and L. Moser, On Abelian permutation groups, Canad. Math. Bull. 8 (1965), 627-630. MR 32 #7631. MR 0190217 (32:7631)
  • [2] G. H. Hardy and E. M. Wright, An introduction to theory of numbers, 4th ed., Oxford Univ. Press, London, 1960. (3rd ed., 1954. MR 16, 673.) MR 0067125 (16:673c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0437509-2
Keywords: Roots of unity, rational polygon
Article copyright: © Copyright 1977 American Mathematical Society

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