Monogenic period equations are cyclotomic polynomials

Gallas, Jason A. C.

doi:10.1142/S0129183120500588

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Monogenic period equations are cyclotomic polynomials

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Gallas, Jason A. C.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Gallas, J. A. C. (2020). Monogenic period equations are cyclotomic polynomials. International Journal of Modern Physics C, 31(4): 2050058. doi:10.1142/S0129183120500588.

Cite as: https://hdl.handle.net/21.11116/0000-0006-E4F4-5

Abstract

We study monogeneity in period equations, psi(e)(x), the auxiliary equations introduced by Gauss to solve cyclotomic polynomials by radicals. All monogenic psi(e)(x) of degrees 4 <= e <= 250 are determined for extended intervals of primes p = e f + 1, and found to coincide either with cyclotomic polynomials or with simple de Moivre reduced forms of cyclotomic polynomials. The former case occurs for p = e + 1, and the latter for p = 2e + 1. For e >= 4, 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.