Modular units, class invariants, and the cuspidal divisor class group

In this talk I will discuss a particular family of modular units constructed using functional solutions to q-difference equations found in the work of Selberg. Arising in this way, these objects are of interest due to various analytic properties, associated q-series identities, combinatorial interpretations, and consequences within partition theory. Dually, we exhibit fundamental roles played by these modular units, many of which are algebraic in nature, including those within class field theory, the cyclotomic theory, the modular function field theory, and the cuspidal divisor class group.