2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76080For a given $x$ we consider the minimum of $\sum_{n\le x} χ(n)/n$ as $χ$ ranges over all quadratic Dirichlet characters. For all large $x$, this minimum is negative and we give upper and lower bounds for it.8 pagesNumber TheoryNegative values of truncations to $L(1,χ)$text