Abstract
We improve the existing upper bound for the quantity |∑ n⩽x a(n 2)|, where a(n 2) is the n 2th Hecke eigenvalue of a normalized holomorphic cusp form (Hecke eigenform) of the full modular group SL(2, ℤ), whenever the weight of the original holomorphic cusp form (Hecke eigenform) lies in a certain range.
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