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

Negative values of truncations to L(1,chi)

Andrew Granville , K. Soundararajan This is my paper

classification math.NT

keywords minimumnegativeboundscharactersconsiderdirichletgivegiven

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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.

Negative values of truncations to L(1,chi)

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