  We describe the possible restrictions of the cotangent bundle \Omega_{\PP^N}
to an elliptic curve C \subset \PP^N. We apply this in positive characteristic
to the computation of the Hilbert-Kunz function of a homogeneous R_+-primary
ideal I \subset R in the graded section ring R = \bigoplus_{n \in \NN}
\Gamma(C, \O(n)).
