Abstract

Let λf(n) denote the nth normalized Fourier coefficient of the primitive holomorphic cusp forms of even integral weight k≥2 for the full modular group SL(2,Z). For x≥1, we are interested in the sums ∑n≤xλf(n)ℓ and ∑a2+b2≤xλf(a2+b2)ℓ. In this paper, we are able to establish the asymptotic formulae for general cases of the power sum for every positive integer ℓ∈N. The special cases of our results improve previous results.

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