Divisor moments of polynomials in Fourier coefficients of modular forms

Wonwoong Lee

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arXiv · 2607.18832

Divisor moments of polynomials in Fourier coefficients of modular forms

Wonwoong Lee

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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.

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Wonwoong Lee. 2026-07-21. Divisor moments of polynomials in Fourier coefficients of modular forms. https://arxiv.org/abs/2607.18832

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