Mahler measures and logarithmic equidistribution

DOI10.5802/aif.2454zbMath1192.14020arXivmath/0612556OpenAlexW2150240286MaRDI QIDQ2390088

Amaury Thuillier, Antoine Chambert-Loir

Publication date: 20 July 2009

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612556

zbMATH Keywords

equidistributionMahler measureArakelov geometryBerkovich spacepoints of small heightarithmetic dynamical system

Mathematics Subject Classification ID

Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Rigid analytic geometry (14G22) Plurisubharmonic functions and generalizations (32U05)

Related Items

Two-variable polynomials with dynamical Mahler measure zero, Height of varieties over finitely generated fields, Points of small height on semiabelian varieties, Faltings height and Néron–Tate height of a theta divisor, Quantitative equidistribution of Galois orbits of small points in the \(N\)-dimensional torus, Higher dimensional essential minima and equidistribution of cycles, A nondensity property of preperiodic points on Chebyshev dynamical systems, Global pluripotential theory over a trivially valued field, Finite orbits for large groups of automorphisms of projective surfaces, Toward Dirichlet's unit theorem on arithmetic varieties, Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry, Heights of hypersurfaces in toric varieties, A dynamical pairing between two rational maps, DEGENERATION OF ENDOMORPHISMS OF THE COMPLEX PROJECTIVE SPACE IN THE HYBRID SPACE, The arithmetic Hodge index theorem and rigidity of dynamical systems over function fields, On Zhang's semipositive metrics, The arithmetic Hodge index theorem for adelic line bundles, Growth of balls of holomorphic sections and energy at equilibrium, Arakelov geometry, heights, equidistribution, and the Bogomolov conjecture, Successive minima of toric height functions, A new formula for Mahler's measure

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Siegel's lemma
• A new capacity for plurisubharmonic functions
• Sur des hauteurs alternatives. I. (On alternative heights. I)
• Diophantine approximation on abelian varieties
• Big line bundles over arithmetic varieties
• Equidistribution of small points on abelian varieties
• Positivity and discretion of algebraic points of curves
• Arithmetic intersection theory
• Heights of polynomials and entropy in algebraic dynamics
• Approximating Zariski decomposition of big line bundles
• Equidistribution of small points
• Arithmetic Hilbert-Samuel theorem
• Equidistribution of small points, rational dynamics, and potential theory
• Equidistribution of subvarieties of small height
• Quantitative uniform distribution of points of small height on the projective line
• About a question of the equidistribution of algebraic numbers.
• Points entiers sur les surfaces arithmétiques
• Continuity of volumes on arithmetic varieties
• Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines
• Local heights of subvarieties over non-archimedean fields
• Heights of Projective Varieties and Positive Green Forms
• Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables
• Existence of the sectional capacity
• Lemmes de zéros dans les groupes algébriques commutatifs
• Positive Line Bundles on Arithmetic Varieties
• Mesures et équidistribution sur les espaces de Berkovich
• Intégration