  Suppose B=F[x,y,z]/h is the homogeneous coordinate ring of a characteristic p
degree 3 irreducible plane curve C with a node. Let J be a homogeneous
(x,y,z)-primary ideal and n -> e_n be the Hilbert-Kunz function of B with
respect to J.
  Let q=p^n. When J=(x,y,z), Pardue (see R. Buchweitz, Q. Chen. Hilbert-Kunz
functions of cubic curves and surfaces. J. Algebra 197 (1997). 246-267) showed
that e_n=(7q^2)/3-q/3-R where R=5/3 if q is congruent to 2 (3), and is 1
otherwise. We generalize this, showing that e_n= (mu q^2) + (alpha q) - R where
R only depends on q mod 3. We describe alpha and R in terms of classification
data for a vector bundle on C. Igor Burban (I. Burban. Frobenius morphism and
vector bundles on cycles of projective lines. 2010. arXiv 1010.0399) provided a
major tool in our proof by showing how pull-back by Frobenius affects the
classification data of an indecomposable vector bundle over C. We are also
indebted to him for pointing us towards Y. A. Drozd, G.-M. Greuel, I. Kashuba.
On Cohen-Macaulay modules on surface singularities. Mosc. Math. J. 3 (2003).
397-418, 742, in which h^0 is described in terms of these classification data.
