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arXiv · 2305.04960

Counting points by height in semigroup orbits

Jason P. Bell·Wade Hindes·Xiao Zhong
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Abstract

We improve known estimates for the number of points of bounded height in semigroup orbits of polarized dynamical systems. In particular, we give exact asymptotics for generic semigroups acting on the projective line. The main new ingredient is the Wiener-Ikehara Tauberian theorem, which we use to count functions in semigroups of bounded degree.

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Jason P. Bell, Wade Hindes, Xiao Zhong. 2023-05-08. Counting points by height in semigroup orbits. https://doi.org/10.4153/s0008414x24000579

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