Moments of Random Multiplicative Functions and Truncated Characteristic Polynomials
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An asymptotic formula for the 2kth moment of a sum of multiplicativeSteinahus variables is given. This is obtained by expressing the momentas a 2k-fold complex contour integral, from which one can extract the lead-ing order term. The 2kth moment of a truncated characteristic polynomial ofa unitary matrix is also computed. This is done by expressing the moment asa combinatoric sum over a restricted region, and then invoking each restric-tion by introducing some complex integral. This gives a 2k-fold integral thatis very similar to the 2kth moment of the sum of multiplicative Steinhausvariables, which in turn gives an asymptotic relation between the two.Similarly, an asymptotic formula is given for the 2kth moment of a sum ofmultiplicative Rademacher variables, and the 2kth moment of the truncatedcharacteristic polynomial of a special orthogonal matrix is found. This givesan asymptotic relation between these two.