Monogenic period equations are cyclotomic polynomials

Jason A. C. Gallas
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Jason A. C. Gallas: Instituto de Altos Estudos da Paraíba, Rua Silvino Lopes 419-2502, João Pessoa 58039-190, Brazil2Complexity Sciences Center, 9225 Collins Ave. Suite 1208, Surfside FL 33154, USA3Max-Planck-Institut für Physik komplexer Systeme, Dresden 01187, Germany

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 04, 1-8

Abstract: We study monogeneity in period equations, ψe(x), the auxiliary equations introduced by Gauss to solve cyclotomic polynomials by radicals. All monogenic ψe(x) of degrees 4≤e≤250 are determined for extended intervals of primes p=ef+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.

Keywords: Quadratic dynamics; monogenic equations; cyclotomic period equations; symbolic computation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120500588

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