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Let λ(n) be the n-th normalized Fourier coefficient of a holomorphic Hecke eigenform f (z) ∈ S k (Γ) for the full modular group. In one of his papers, Sankaranarayanan mentioned that it is an open problem to give a non-trivial estimate for the sum of λ(n) over cubes, i.e. n x λ(n 3 ). In this paper, we are able to use the analytic properties of symmetric power L-functions to solve his problem. More precisely, we prove that n x λ(n 3 ) x 3 4 +ε , n x λ(n 4 ) x 7 9 +ε .

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Cited by 8 publications

References 10 publications

The cancellation of Fourier coefficients of cusp forms over different sparse sequences

The cancellation of Fourier coefficients of cusp forms over different sparse sequences

On the fourth moment of coefficients of symmetric square L-function

On an open problem of Sankaranarayanan

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