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Bounds for Moments of Twisted Fourier coefficients of Modular Forms

Bounds for Moments of Twisted Fourier coefficients of Modular Forms

We establish upper bounds for shifted moments of modular $L$-functions to a fixed modulus as well as quadratic twists of modular $L$-functions under the generalized Riemann hypothesis. Our results are then used to establish bounds for moments of sums involving with Fourier coefficients of a given modular form twisted by …