Moments of Random Multiplicative Functions and Truncated Characteristic Polynomials

We give an asymptotic formula for the 2kth moment of a sum of multiplicative Steinhaus variables. This was recently computed independently by Harper, Nikeghbali and Radziwiłł. We also compute the 2kth moment of a truncated characteristic polynomial of a unitary matrix, and this is seen to be asymptotically equivalent with the moments of Steinhaus variables. Similar results for multiplicative Rademacher variables are given with the corresponding random matrix average being over the special orthogonal group.