Damian Roessler: On a canonical class of Green currents for the unit sections of
Abstract: We show that on any abelian scheme over a complex
quasi-projective smooth variety, there is a Green current for the
zero-section, which is axiomatically determined up to $\partial$ and
$\bar\partial$-exact differential forms. This current generalizes the
Siegel functions defined on elliptic curves. We prove generalizations of
classical properties of Siegel functions, like distribution relations,
limit formulae and reciprocity laws.