Moments of random multiplicative functions and truncated characteristic polynomials

2015/05/13 by Heap, Winston, Lindqvist, Sofia · 2 citations
#FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.1505.03378

Abstract

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. This provides an asymptotic equivalence with the moments of Steinhaus variables. Similar results for multiplicative Rademacher variables are given.

Cited by

• Counting 2 × 2 integer matrices with a given determinant
• On the limiting distribution of sums of random multiplicative functions

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