Mean squares of quadratic twists of the Fourier coefficients of modular forms
Abstract
In this paper, we evaluate asymptotically a smoothed version of the sum \[ *Σd ≤ X ( Σn ≤ Y λf(n)(8dn))2, \] where ( 8d· ) is the Kronecker symbol, *Σ denotes a sum over positive odd square-free integers and λf(n) are Fourier coefficients of a given modular form f.
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