  Let R be a formal power series ring over a perfect field k of prime
characteristic p, and let m be the maximal ideal of R. Suppose f is a non-zero
element in m. In this paper, we introduce a function xi (x) associated with a
hypersurface defined on the closed interval [0, 1] in R. The Hilbert-Kunz
function and the F-signature of a hypersurface appear as the values of our
function xi (x) on the interval s endpoints.
