Negative values of truncations to $L(1,\chi)$

Andrew Granville; K. Soundararajan

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Negative values of truncations to $L(1,\chi)$

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arxiv math/0508361 v1 pith:43WRAB64 submitted 2005-08-18 math.NT

Andrew Granville , K. Soundararajan This is my paper · ORCID

classification math.NT

keywords minimumnegativeboundscharactersconsiderdirichletgivegiven

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abstract

For a given $x$ we consider the minimum of $\sum_{n\le x} \chi(n)/n$ as $\chi$ ranges over all quadratic Dirichlet characters. For all large $x$, this minimum is negative and we give upper and lower bounds for it.

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