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Moments of random multiplicative functions, III: A short review

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arxiv 2410.11523 v1 pith:FNJXCQ63 submitted 2024-10-15 math.NT math.PR

Adam J. Harper This is my paper · ORCID
classification math.NTmath.PR
keywords functionsmomentsmultiplicativerandomreviewshortareabackground
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abstract

We give a short review of recent progress on determining the order of magnitude of moments $\mathbb{E}|\sum_{n \leq x} f(n)|^{2q}$ of random multiplicative functions, and of closely related issues. We hope this can serve as a concise introduction to some of the ideas involved, for those who may not have too much background in the area.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A sharp almost sure upper bound for partial sums of random multiplicative functions

    math.NT 2026-07 conditional novelty 8.0 of 10

    For both Steinhaus and Rademacher random multiplicative functions, almost surely |sum_{n≤x} f(n)| ≪ sqrt(x)(log log x)^{1/4+ε}, matching Harper's lower bound.

  2. Central limit theorems for random multiplicative functions over function fields

    math.NT 2025-11 conditional novelty 6.0 of 10

    A sufficiently large polynomial set with asymptotically trivial multiplicative energy yields a complex Gaussian limit for Steinhaus random multiplicative sums; short intervals, few prime factors, shifted primes, and r...

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