Mathematical Research Letters

Volume 11, Issue 4, July 2004 pp. 453-466.

Pfaffian equations satisfied by differential modular forms

Authors: Alexandru Buium
Author institution: University of New Mexico

Summary: The ring of (ordinary) isogeny covariant differential modular forms introduced in \cite{difmod} was shown in \cite{Barcau} to be described by two basic forms introduced in \cite{difmod} and \cite{Barcau} respectively. We prove that these two forms satisfy a simple triangular system of Pfaffian equations (in characteristic zero). The equation giving the form in \cite{Barcau} is ``integrable by quadratures'' which gives a closed form expression for this form; the equation giving the form in \cite{difmod} is shown not to be ``integrable by quadratures''.

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