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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Cyclotomic resultants

Authors: D. H. Lehmer and Emma Lehmer
Journal: Math. Comp. 48 (1987), 211-216
MSC: Primary 11T21
MathSciNet review: 866110
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Abstract: This paper examines the eth power character of the divisors of two cyclotomic period polynomials of degree $ {e_1}$ and $ {e_2}$. The special cases $ {e_1} = 2$ and $ {e_2} = 3,4$, are considered in detail. As corollaries one finds new conditions for cubic and quartic residuacity.

The computational method consists in representing cyclotomic numbers in the form $ {c_1}\zeta + {c_2}{\zeta ^2} + \cdots + {c_{p - 1}}{\zeta ^{p - 1}}$, where $ \zeta = {e^{2\pi i/p}}$. Multiplication is reduced to addition and subtraction, which are carried out in a multi-precision system.

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Article copyright: © Copyright 1987 American Mathematical Society