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Alina Ostafe,
Lukas Pottmeyer, and
Igor E. Shparlinski
Perfect powers in value sets and orbits of polynomials
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| Published: |
June 17, 2021. |
| Keywords: |
arithmetic dynamics, perfect powers. |
| Subject: |
11R27, 37P15. |
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Abstract
We show the finiteness of perfect powers in orbits of polynomial dynamical systems over an algebraic number field. We also obtain similar results for perfect powers represented by ratios of consecutive elements in orbits. Assuming the abc-Conjecture for number fields, we obtain a finiteness result for powers in ratios of arbitrary elements in orbits.
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| Acknowledgements
The work of A.O. and I.S. was supported in part by the Australian Research Council Grant DP180100201.
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| Author information
Alina Ostafe:
School of Mathematics and Statistics
University of New South Wales
Sydney NSW 2052, Australia
alina.ostafe@unsw.edu.au
Lukas Pottmeyer:
Fakultät für Mathematik
Universität Duisburg-Essen
45117 Essen, Germany
lukas.pottmeyer@uni-due.de
Igor E. Shparlinski:
School of Mathematics and Statistics
University of New South Wales
Sydney NSW 2052, Australia
igor.shparlinski@unsw.edu.au
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