I will define a quasipolynomial and its generating function. In a convolution of quasipolynomials with degrees d and e and periods p and q, the leading term (degree e+f+1 ) has period gcd(p,q) , smaller than the expected value of lcm(p,q) . Sometimes, this leading term is zero; I will characterize such cases by means of the null space of a circulant matrix.