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arXiv · 2609.20460

Low moments of automorphic random multiplicative function sums

Sun-Kai Leung
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Abstract

We determine the order of the low moments of partial sums of random multiplicative functions associated with Euler products of bounded degree whose unitary local parameters satisfy a prime-square cancellation condition, thereby generalizing Harper's seminal work. The result applies to irreducible compact-group representations of unitary or symplectic type, including the higher-rank Sato--Tate model $SU(d)$ and the odd symmetric-power Sato--Tate model $\operatorname{Sym}^{m}SU(2)$.

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Sun-Kai Leung. 2026-09-17. Low moments of automorphic random multiplicative function sums. https://arxiv.org/abs/2609.20460

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