Lower Bounds on High Moments of Twisted Fourier coefficients of Modular Forms

2025/11/04 by Gao, Peng, Zhao, Liangyi · 1 citation
Mathematics · #11L40 #11M06 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.02344

openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

For any large prime q, x ≤ 1 and any real k≥ 2, we prove a lower bound for the following 2k-th moment ∑_\substackχ∈ X_q^* | ∑_{n≤ x} χ(n)λ(n)|^2k, where X_q^* denotes the set of primitive Dirichlet characters modulo q and λ(n) the Fourier coefficients of a fixed modular form. The bound we obtain is sharp up to a constant factor under the generalized Riemann Hypothesis.

Citations

• Bounds for Moments of Twisted Fourier coefficients of Modular Forms
• High moments of theta functions and character sums
• Bounds for moments of modular L-functions to a fixed modulus

Cited by

• Upper Bounds for low moments of twisted Fourier coefficients of modular forms

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