Cyclotomic resultants
Authors:
D. H. Lehmer and Emma Lehmer
Journal:
Math. Comp. 48 (1987), 211216
MSC:
Primary 11T21
MathSciNet review:
866110
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: This paper examines the eth power character of the divisors of two cyclotomic period polynomials of degree and . The special cases and , 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 , where . Multiplication is reduced to addition and subtraction, which are carried out in a multiprecision system.
 [1]
Paul Bachmann, Die Lehre von der Kreistheilung, B. G. Teubner, Leipzig, 1872, pp. 210213, 224230.
 [2]
Ronald
J. Evans, The octic periodic
polynomial, Proc. Amer. Math. Soc.
87 (1983), no. 3,
389–393. MR
684624 (84b:10055), http://dx.doi.org/10.1090/S00029939198306846242
 [3]
E. E. Kummer, "Über die Divisoren gewisser Formen der Zahlen welche aus der Theorie der Kreistheilung entstehen," J. Reine Angew. Math., v. 30, 1846, pp. 107116, Collected papers, v. 1, pp. 193239.
 [4]
J. J. Sylvester, "On the multisection of roots of unity," Johns Hopkins Univ. Circular, v. 1, 1881, pp. 150151, Collected papers, v. 3, pp. 477478.
 [1]
 Paul Bachmann, Die Lehre von der Kreistheilung, B. G. Teubner, Leipzig, 1872, pp. 210213, 224230.
 [2]
 Ronald J. Evans, "The octic period polynomial," Proc. Amer. Math. Soc., v. 87, 1983, pp. 389393. MR 684624 (84b:10055)
 [3]
 E. E. Kummer, "Über die Divisoren gewisser Formen der Zahlen welche aus der Theorie der Kreistheilung entstehen," J. Reine Angew. Math., v. 30, 1846, pp. 107116, Collected papers, v. 1, pp. 193239.
 [4]
 J. J. Sylvester, "On the multisection of roots of unity," Johns Hopkins Univ. Circular, v. 1, 1881, pp. 150151, Collected papers, v. 3, pp. 477478.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
11T21
Retrieve articles in all journals
with MSC:
11T21
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708661101
PII:
S 00255718(1987)08661101
Article copyright:
© Copyright 1987
American Mathematical Society
