Differential modular forms over totally real fields of non zero integral weights

TL;DR

This paper constructs differential modular forms over totally real fields with non-zero integral weights, extending classical theories and generalizing Buium's work to a broader setting.

Contribution

It introduces a new construction of differential modular forms over totally real fields with non-zero integral weights, expanding the scope beyond classical cases.

Findings

Construction of differential modular forms over totally real fields.

Extension of Buium's classical construction to non-zero weights.

Generalization to non-classical, higher-order forms.

Abstract

In this article, we construct differential modular forms for compact Shimura curves over totally real fields bigger than rational of non-zero integral weights that is not classical (of order zero) generalizing the construction of Buium [8].