Monogenic period equations are cyclotomic polynomials
2020 ◽
Vol 31
(04)
◽
pp. 2050058
◽
Keyword(s):
We study monogeneity in period equations, [Formula: see text], the auxiliary equations introduced by Gauss to solve cyclotomic polynomials by radicals. All monogenic [Formula: see text] of degrees [Formula: see text] are determined for extended intervals of primes [Formula: see text], and found to coincide either with cyclotomic polynomials or with simple de Moivre reduced forms of cyclotomic polynomials. The former case occurs for [Formula: see text], and the latter for [Formula: see text]. For [Formula: see text], we conjecture all monogenic period equations to be cyclotomic polynomials. Totally real period equations are of interest in applications of quadratic discrete-time dynamical systems.
2009 ◽
Vol 19
(10)
◽
pp. 3283-3309
◽
Keyword(s):
Keyword(s):
1992 ◽
Vol 12
(1)
◽
pp. 153-183
◽