Abstract
In this paper we investigate difference equations related to number theory. We apply a criterion to reduce these hereditary difference equations to finite length. The solutions are polynomials in one variable. We analyze the solutions with respect to convergence, periodicity, and boundedness. As an example we obtain and study Chebyshev polynomials of the second kind. We also apply Poincaré’s theorem to transform a non-autonomous difference equation to an autonomous version.
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Acknowledgments
We thank the organisers of the conference, especially Steve Baigent, for their invitation and their excellent job and the reviewer for several useful comments.
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HEIM, B., Neuhauser, M. (2020). Difference Equations Related to Number Theory. In: Baigent, S., Bohner, M., Elaydi, S. (eds) Progress on Difference Equations and Discrete Dynamical Systems. ICDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-030-60107-2_11
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DOI: https://doi.org/10.1007/978-3-030-60107-2_11
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