Periodicity in Quasipolynomial Convolution

Abstract

The leading term of a convolution of quasipolynomials with periods $p$ and $q$ is periodic with period $\gcd(p,q)$, smaller than expected. The degree of the convolution is usually $d+e+1$; we characterize the exceptions. To do this we need to characterize the null space of a circulant matrix.