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Divisor moments of polynomials in Fourier coefficients of modular forms
Abstract
We study higher moments of the divisor function evaluated at polynomial expressions in the Fourier coefficients of a non-CM newform. The logarithmic exponent appearing in our estimates depends only on the number of irreducible factors of the polynomial and remains unchanged under a Sato--Tate restriction. The proof combines an effective Chebotarev theorem, or an effective Chebotarev--Sato--Tate theorem, with the arithmetic of joint cycle types and a mean value estimation for multivariable multiplicative functions with Frobenian support.
Related
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BibTeX
@misc{lee2026divisor,
title = {{Divisor moments of polynomials in Fourier coefficients of modular forms}},
author = {Wonwoong Lee},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.18832},
eprint = {2607.18832},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18832},
}
RIS
TY - UNPB
TI - Divisor moments of polynomials in Fourier coefficients of modular forms
AU - Wonwoong Lee
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2607.18832
UR - https://arxiv.org/abs/2607.18832
AB - We study higher moments of the divisor function evaluated at polynomial expressions in the Fourier coefficients of a non-CM newform. The logarithmic exponent appearing in our estimates depends only on the number of irreducible factors of the polynomial and remains unchanged under a Sato--Tate restriction. The proof combines an effective Chebotarev theorem, or an effective Chebotarev--Sato--Tate theorem, with the arithmetic of joint cycle types and a mean value estimation for multivariable multiplicative functions with Frobenian support.
ER -