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

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Arakelov theory

heights

cusp forms

pluripotential theory

Monge-Ampere operators

finite energy functions

cusp forms

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