The extension theorem for the Lee and Euclidean weights over Z/pkZ

The Lee and Euclidean weights have the extension property over the local rings $\mathbb{Z}/p^k\mathbb{Z}$, p prime. The non-vanishing of certain Fourier coefficients is established by expressing the coefficients in terms of generalized Bernoulli numbers and making use of knowledge of the locations of zeros of Dirichlet L-functions.