F-signature function of quotient singularities

We study the shape of the F-signature function of a d-dimensional quotient singularity k〚x1,…,xd〛G, and we show that it is a quasi-polynomial. We prove that the second coefficient is always zero and we describe the other coefficients in terms of invariants of the finite acting group G⊆Gl(d,k). When G is cyclic, we obtain more specific formulas for the coefficients of the quasi-polynomial, which allow us to compute the general form of the function in several examples.