Structure factor of Cantor sets

We write down an infinite-product expression for the structure factor S(k) of a one-parameter family of Cantor sets. From this expression, we find the positions of the zeros and approximate expressions for the positions of the maxima of S(k). Mellin transforms and two averaging methods are used to determine aspects of the asymptotic behavior of S(k) for large k. Two distinct power laws are obtained, depending on the averaging method utilized.