H. Helfgott

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math.NT2025

Optimal bounds for sums of non-negative arithmetic functions

AndrÃ©s Chirre, Harald AndrÃ©s Helfgott

Let $A (s) = \sum_{n} a_{n} n^{- s}$ be a Dirichlet series admitting meromorphic continuation to the complex plane. Assume we know the location of the poles of $A (s)$ with $|\Im s| \leq…

math.NT2025

Optimal bounds for sums of bounded arithmetic functions

Let $A (s) = \sum_{n} a_{n} n^{- s}$ be a Dirichlet series with meromorphic continuation. Say we are given information on the poles of $A (s)$ with $∣ℑ s ∣ \leq T$ for some large constan…