Mean squares of quadratic twists of the Fourier coefficients of modular forms

2025/06/27 by Gao, Peng, Zhao, Yuetong · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.22256

Abstract

In this paper, we evaluate asymptotically a smoothed version of the sum \sideset^*∑_{d ≤ X} ( ∑_{n ≤ Y} λ_f(n)((8d)/(n)))², where ( (8d)/(⋅) ) is the Kronecker symbol, \sideset^*∑ denotes a sum over positive odd square-free integers and λ_f(n) are Fourier coefficients of a given modular form f.

Citations

• Bounds for moments of quadratic character sums and theta functions
• Bounds for Moments of Twisted Fourier coefficients of Modular Forms
• Shifted moments of quadratic Dirichlet L-functions
• High moments of theta functions and character sums
• Moments of quadratic twists of modular L-functions
• The mean square of real character sums
• Sharp conditional bounds for moments of the Riemann zeta function
• Moments of the Riemann zeta-function
• On sums of Fourier coefficients of cusp forms
• Transition mean values of real characters
• Nonvanishing of Quadratic Dirichlet L-Functions at S = &#189

Cited by

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

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• The mean square of real character sums
• Lower Bounds on High Moments of Twisted Fourier coefficients of Modular Forms
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• Bounds for Moments of Twisted Fourier coefficients of Modular Forms