Function Field Modular Forms and Higher Derivations, by Yukiko Uchino, Takakazu Satoh

This paper has now appeared in Math. Ann. Vol.311, pp. 439-466 (1998) and so the dvi version has been removed. From the abstract:

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 <>