Abstract: Classically, Ligozat's theorem provides a complete characterization of modular units on Hecke modular curves over the rational numbers in terms of eta quotients. In the function field setting, we investigate an analogous phenomenon by studying the roots of Delta quotients. In this talk, we determine the group of all such roots for levels that are square-free except for at most one prime divisor. As an application, we provide a complete description of the structure of the rational cuspidal divisor class group in specific cases. This is joint work with Shang-Yang Kevin Ho.

 

Organizer: Fu-Tsun Wei (NTHU)