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- W4288335071 abstract "The Arakelov-Zhang pairing $langlepsi,phirangle$ is a measure of the dynamical distance between two rational maps $psi$ and $phi$ defined over a number field $K$. It is defined in terms of local integrals on Berkovich space at each completion of $K$. We obtain a simple expression for the important case of the pairing with a power map, written in terms of integrals over Julia sets. Under certain disjointness conditions on Julia sets, our expression simplifies to a single canonical height term; in general, this term is a lower bound. As applications of our method, we give bounds on the difference between the canonical height $h_phi$ and the standard Weil height $h$, and we prove a rigidity statement about polynomials that satisfy a strong form of good reduction." @default.
- W4288335071 created "2022-07-29" @default.
- W4288335071 creator A5073686311 @default.
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- W4288335071 date "2019-06-06" @default.
- W4288335071 modified "2023-10-16" @default.
- W4288335071 title "The Arakelov-Zhang pairing and Julia sets" @default.
- W4288335071 doi "https://doi.org/10.48550/arxiv.1906.02654" @default.
- W4288335071 hasPublicationYear "2019" @default.
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