Cyclotomic Resultants
Derrick Henry Lehmer, Emma T. Lehmer · Mathematics of Computation · 1987
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.