Giovanni De Gaetano (Humboldt Universität zu Berlin)
The determinant of the Laplacian Delta_k on k-differentials,
or on automorphic forms of weight k, on a compact Riemann surface played
an important role in the mathematical physics literature in the late '80s.
It turns out that the same object in the non-compact setting has an
arithmetic significance, but its natural definition is not convergent. In
this talk, after a review of the classical theory, we examine two
alternative definitions and related convergence results; the crucial point
to be examined is the behavior of the associated heat kernel at the missing
points.
