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, Volume 59, Issue 3, pp 375–389 | Cite as

Character coordinates and annihilators of cyclotomic numbers

  • Kurt Girstmair


The object of this paper is a representation theoretical approach to the problem of determining allQ-linear relations between conjugate numbers in a cyclotomic field. We apply our method to relations between the numbers cot(m)(πk/n), tan(m)(πk/n), cosec(m)(2πk/n), sec(m)(2πk/n), respectively, where m is≥0 and (k,n)=1. Thereby we complete previous work of Chowla, Hasse, Jager-Lenstra, and others.


Number Theory Theoretical Approach Algebraic Geometry Topological Group Cyclotomic Field 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Kurt Girstmair
    • 1
  1. 1.Institut für MathematikUniversität InnsbruckInnsbruckAustria

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