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- Title
An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms.
- Authors
Berman, Robert J.; Freixas i Montplet, Gerard
- Abstract
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–Kühn. 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.
- Subjects
HILBERT functions; CUSP forms (Mathematics); HERMITIAN forms; SINGULAR integrals; MODULAR forms
- Publication
Compositio Mathematica, 2014, Vol 150, Issue 10, p1703
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X14007325