Rational Ehrhart quasi-polynomials

Ehrhartʼs famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors. It turns out that the number of integral points can still be written as a rational quasi-polynomial. Furthermore, the coefficients of this rational quasi-polynomial are piecewise polynomial functions and related to each other by derivation.