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

Robert Berman (Institutionen för matematiska vetenskaper, matematik) ; G. F. I. Montplet
Compositio Mathematica (0010-437X). Vol. 150 (2014), 10, p. 1703-1728.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Arakelov theory, heights, cusp forms, pluripotential theory, Monge-Ampere operators, finite energy functions



Denna post skapades 2014-12-29.
CPL Pubid: 209142

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur