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Character coordinates and annihilators of cyclotomic numbers

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Abstract

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.

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  1. Institut für Mathematik, Universität Innsbruck, Technikerstraße 25, A-6020, Innsbruck, Austria

    Kurt Girstmair

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  1. Kurt Girstmair
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Girstmair, K. Character coordinates and annihilators of cyclotomic numbers. Manuscripta Math 59, 375–389 (1987). https://doi.org/10.1007/BF01174800

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