Bounds for integral moments of quadratic twists of Fourier coefficients of modular forms

2025/09/24 by Gao, Peng, Zhao, Yuetong
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.20085

Abstract

In this paper, we obtain under the assumption of the Generalized Riemann Hypothesis upper bounds for all high integral moments of sums of Fourier coefficients of a given modular form twisted by quadratic Dirichlet characters. We show the bounds are optimal by establishing unconditionally the corresponding lower bounds for all even integer moments.

Citations

• Mean squares of quadratic twists of the Fourier coefficients of modular forms
• Shifted moments of quadratic Dirichlet L-functions

Related

• Bounds for Moments of Twisted Fourier coefficients of Modular Forms
• Lower Bounds on High Moments of Twisted Fourier coefficients of Modular Forms
• Upper Bounds for low moments of twisted Fourier coefficients of modular forms
• Additive Twists of Fourier Coefficients of Modular Forms
• Bounds for moments of quadratic Dirichlet character sums of prime moduli