PreprintCC BY 4.0arXiv
Low moments of automorphic random multiplicative function sums
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 SymmSU(2).
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BibTeX
@misc{leung2026moments,
title = {{Low moments of automorphic random multiplicative function sums}},
author = {Sun-Kai Leung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20460},
eprint = {2609.20460},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20460},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Low moments of automorphic random multiplicative function sums
AU - Sun-Kai Leung
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20460
UR - https://arxiv.org/abs/2609.20460
AB - 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 Sym^mSU(2).
ER -