Adam Biggs (University of Manchester)
adam.biggs-2@postgrad.manchester.ac.uk
We shall give an interpretation of the second Eisenstein series $E_2$ as defining a unique ${\mathop{SL}}_2(\mathbb Z)$-invariant differential operator and as a connection on the space $\Omega^{1,0}$ of holomorphic forms on $H$. We shall then explore some simple consequences of this identification and study similar differential operators for congruence subgroups.