Title: Dedekind sums for cofinite Fuchsian groups
Speaker: Claire Burrin (Rutgers University)
Abstract: Dedekind sums, studied since the late 19th century, are closely related to an amazing variety of objects ranging through combinatorics, geometry, number theory, and physics. Among those, we simply mention the discriminant form from the classical theory of modular forms, and winding and linking numbers for modular geodesics. For each cusp of a cofinite Fuchsian group, there is a natural construction from the theory of automorphic forms that can be used to define generalized Dedekind sums. We will show that these generalized Dedekind sums obey certain reciprocity laws, and discuss their relation to winding numbers for closed geodesics on hyperbolic surfaces.
Seminar URL: https://research.math.osu.edu/numbertheory/number.php
