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Monogenic period equations are cyclotomic polynomials

Author

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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)

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.

Suggested Citation

  • Jason A. C. Gallas, 2020. "Monogenic period equations are cyclotomic polynomials," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-8, February.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:04:n:s0129183120500588
    DOI: 10.1142/S0129183120500588
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