In the study of modular forms, Jacobi forms, etc. over the complex numbers, differential operators occasionally play an important role. For function field modular forms whose values lie in a positive characteristic field, differential is not a powerful tool. For example, locally analytic functions are annihilated by $p$-times differential, where $p$ is the characteristic. Instead, we use a continuous higher derivation. As an application, we construct the Cohen bracket for function field modular forms. We also study a function field analogue of two variable functions which behave like a Jacobi form only under the action of modular group.

Yukiko Uchino, Takakazu Satoh <tsatoh@rimath.saitama-u.ac.jp>