An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms

DOI10.1112/S0010437X14007325zbMath1316.14048arXiv1209.0996MaRDI QIDQ2931764

Gerard Freixas i Montplet, Robert J. Berman

Publication date: 27 November 2014

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.0996

zbMATH Keywords

heightscusp formsArakelov theorypluripotential theoryfinite energy functionsMonge-Ampere operators

Mathematics Subject Classification ID

Modular and Shimura varieties (14G35) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Holomorphic bundles and generalizations (32L05) Complex Monge-Ampère operators (32W20)

Related Items (8)

Uniform Sup-Norm Bounds on Average for Cusp Forms of Higher Weights ⋮ Quotient of Bergman kernels on punctured Riemann surfaces ⋮ The probabilistic vs the quantization approach to Kähler-Einstein geometry ⋮ Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's ``hypothèse fondamentale ⋮ Bergman kernels on punctured Riemann surfaces ⋮ Introduction to arithmetic Hilbert-Samuel theorems ⋮ The closures of test configurations and algebraic singularity types ⋮ Effective sup-norm bounds on average for cusp forms of even weight

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