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$\sum_n a_n/n$, $\sum_n a_n/n^\rho$, $\sum_n a_n$… Tauberian theorems?
In analytic number theory, it is common to prove that $$\sum_{n\leq N} \frac{a_n}{n} = o(\log N)\tag{$\star$}\label{476699_star}$$ for some sequence $\{a_n\}_{n=1}^\infty$, $a_n\in \mathbb{C}$. (It is ...
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