An inner product on adelic measures with applications to the Arakelov-Zhang pairing

DOI10.1090/TRAN/9231MaRDI QIDQ6629481

[[Person:6377664|Author name not available (Why is that?)]]

Publication date: 30 October 2024

Published in: (Search for Journal in Brave)

zbMATH Keywords

arithmetic dynamicsArakelov-Zhang pairingadelic measures

Mathematics Subject Classification ID

Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30)

Cites Work

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• Energy integrals and small points for the Arakelov height
• Brolin's equidistribution theorem in \(p\)-adic dynamics.
• Common preperiodic points for quadratic polynomials
• Uniform Manin-Mumford for a family of genus 2 curves
• Equidistribution of small points, rational dynamics, and potential theory
• Invariant sets under iteration of rational functions
• Quantitative uniform distribution of points of small height on the projective line
• The Arithmetic of Elliptic Curves
• An invariant measure for rational maps
• Dynamics in One Non-Archimedean Variable
• The Arakelov-Zhang pairing and Julia sets
• Canonical heights, transfinite diameters, and polynomial dynamics
• The distribution of Galois orbits of points of small height in toric varieties
• A dynamical pairing between two rational maps
• Mesures et équidistribution sur les espaces de Berkovich
• Minimums successifs des variétés toriques projectives
• Théorie ergodique des fractions rationnelles sur un corps ultramétrique

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