Isogeny covariant differential modular forms modulo \(p\). (English) Zbl 1039.11036
Summary: An interesting theory arises when the classical theory of modular forms is expanded to include differential analogs of modular forms. One of the main motivations for expanding the theory of modular forms is the existence of differential modular forms with a remarkable property, called isogeny covariance, that classical modular forms cannot possess. Among isogeny covariant differential modular forms there exists a particular modular form that plays a central role in the theory. The main result presented in the article is the explicit computation modulo \(p\) of this fundamental isogeny covariant differential modular form.
MSC:
11F85 | \(p\)-adic theory, local fields |
11F11 | Holomorphic modular forms of integral weight |
11G05 | Elliptic curves over global fields |
11F23 | Relations with algebraic geometry and topology |