Abstract
Let α(n) denote the Fourier coefficients of cusp forms or the number of divisors of n. Estimates of the typeare shown, uniformly in q ≤ X. The methods can be extended to other arithmetic functions, for example, the number of representations of n as a sum of two squares or k-free numbers. As an application, sums of the type ∑ n ≤ X α(n) ψ(n) for any q-periodic function ψ can be estimated non-trivially.
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