New York Journal of Mathematics
Volume 25 (2019), 1091-1111


Jorge Mello

On quantitative estimates for quasiintegral points in orbits of semigroups of rational maps

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Published: October 15, 2019.
Keywords: Integral points on orbits, arithmetic dynamics, quantitative estimates.
Subject: Primary 37P15, Secondary 11B37, 11G99, 14G99.

We give quantitative bounds for the number of quasi-integral points in orbits of semigroups of rational maps under some conditions, generalizing previous work of Hsia and Silverman (2011) for orbits generated by the iterations of one rational map.


I would like to say especially thanks to Alina Ostafe, Igor Shparlinski and John Roberts for encouraging me to think in this problem, and I am very grateful for the much helpful suggestions of Igor Shparlinski, and every clarifying conversation that we had about this research. I also am very grateful for the Referee for so helpful suggestions and comments. I am very thankful to Australian Research Council Discovery Grant DP180100201 and UNSW for supporting me in this research.

Author information

Jorge Mello:
University of New South Wales
School of Mathematics and Statistics
UNSW Sydney, NSW, 2052, Australia