Geodesic
Counting points by height in semigroup orbits
Canadian journal of mathematics, Tome 77 (2025) no. 6, pp. 2061-2082

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DOI

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.
DOI : 10.4153/S0008414X24000579
Mots-clés : arithmetic dynamics, semigroup dynamics, heights 
Bell, Jason P.; Hindes, Wade; Zhong, Xiao. Counting points by height in semigroup orbits. Canadian journal of mathematics, Tome 77 (2025) no. 6, pp. 2061-2082. doi: 10.4153/S0008414X24000579
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     title = {Counting points by height in semigroup orbits},
     journal = {Canadian journal of mathematics},
     pages = {2061--2082},
     year = {2025},
     volume = {77},
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     doi = {10.4153/S0008414X24000579},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X24000579/}
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