Ulf Kühn
Preprint series: Institut für Mathematik, Humboldt-Universität
zu Berlin (ISSN 0863-0976), 2001-12, 23 pages
MSC 2000
-
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
-
11F66 Dirichlet series and functional equations in
-
11G40 $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer
conjecture
Abstract
We
give an expression for the value of the Neron-Tate height pairing of two
divisors on an algebraic curve which involves special values of certain
Dirichlet series associated to finite index subgroups of the modular group.
Keywords:Neron-Tate
heights, Arakelov geometry, modular curves, Eisenstein series, scattering
matrix, noncongruence subgroups