An arithmetic Hilbert-Samuel theorem for singular hermitian line bundles and cusp forms
Journal article, 2014

We prove arithmetic Hilbert-Samuel type theorems for semi-positive singular hermitian line bundles of finite height. This includes the log-singular metrics of Burgos-Kramer-Kuhn. The results apply in particular to line bundles of modular forms on some non-compact Shimura varieties. As an example, we treat the case of Hilbert modular surfaces, establishing an arithmetic analogue of the classical result expressing the dimensions of spaces of cusp forms in terms of special values of Dedekind zeta functions.

cusp forms

finite energy functions

pluripotential theory

Monge-Ampere operators


Arakelov theory


Robert Berman

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

G. F. I. Montplet

Pierre and Marie Curie University (UPMC)

Compositio Mathematica

0010-437X (ISSN) 1570-5846 (eISSN)

Vol. 150 10 1703-1728

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